I think this question is distinct from those asking what is reincarnated. I understand the distinction between the mindstream and a soul, and the simile of passing on a flame. I also understand that an association is made between a mindstream and human form, most often in the womb. What is it that makes and maintains this mental-physical association endure throughout a human lifetime? Why is there a tendency for the association to result in a first-person perspective/sense of self?
There is no single mindstream, the illusion of identity is a mind-made imputation.
Instead, mind can be seen as an infinitely spanning graph of interconnected concurrent processes.
Seeing a single identity in that is exactly the result of ignorant reification that Buddha and Buddhism are trying to save the "sentient beings" from.
The way a sense of single-identity develops is described in the teaching of twelve nidanas. In modern terms it's a self-perpetuating semiotic process that develops from vague to increasingly more concrete delineation of entities (objects and the subject). To boil it down to a single principle, pursuing desirable objects is the act that by implication(inference) leads to semiotic emergence of "that" (object) and "this" (subject). This self-emergent tendency is then reinforced by the culture that carries it on from generation to generation.
What is it that makes and maintains this mental-physical association endure throughout a human lifetime?
It's an ongoing conditioned process whereby a state conditions the next. Imagine a line of domino's. You tip one over, that one tips the next over and so on. There are the domino's; and there are different (invisible) forces playing a part in how the next domino is tipped. (It's not a great comparison though. Cause the domino's in the line are already there when in actuality that's not the case. But I haven't found a better comparison yet, the candle simile doesn't work for me.)
So, a state of matter-mind-combination ceases and makes room for the appearing of the next matter-mind-combination (at least in the sense realm). The ceasing of the mind-matter-combination is a condition for the arising of the next. But so are different other conditioning forces.
The Patthana (last part of the Abhidhamma) explains 24 different conditioning forces that play a role in the arising of the next states and the maintaining of the process. Important is also to understand that there are always several conditioning forces active, not just one. You might want to read this book. Or just the chapter of the Patthana in the compendium of the Abhidhamma, by Bhikkhu Bodhi.
By the way, at a certain point it's possible to see the conditioning of this ongoing arising and ceasing in meditation. It's fascinating, at least for me.
Why is there a tendency for the association to result in a first-person perspective/sense of self?
That's due to conditioning. Delusion (which is there when one experiences this first-person sense of self) is basically embedded in every newly arising matter-mind-combo. It has to be broken down, replaced by new conditioning.
The practice of what's usually called vipassana meditation (or meditation based on the Satipatthana sutta) makes this possible. From own experience I can say that with vipassana the experience of first person becomes the experience of being the observer (2nd person) of the ongoing arising and ceasing of the matter-mind-combo. And later the experience shifts even further away to more and more neutral, so the feeling of being the observer also drops away. By then there is no more experience of liking, disliking; no identification with what ever khanda, no kilesa and so on. (Upekkha nana).
So, it's a matter of replacing old conditioning with new one. That can take time though. Depending, again, on the way your mind stream is conditioned and how quickly your mind can let go of old ideas and so on.
Hope this helps a bit.
This mental-physical association you speak of, is called namarupa or name-and-form in Buddhism. In SN 12.2, it is described as:
"And what is name-&-form? Feeling, perception, intention, contact, & attention: This is called name. The four great elements, and the form dependent on the four great elements: This is called form. This name & this form are called name-&-form.
In dependent origination, the requisite condition of aging and death is birth. The requisite condition of birth is becoming. The requisite condition of becoming is clinging. The requisite condition of clinging is craving. The requisite condition of craving is feeling. The requisite condition of feeling is contact. The requisite condition of contact is name-and-form. This is according to DN 15.
But what is the requisite condition of name-and-form?
According to the Maha-nidana Sutta (DN 15):
"'From consciousness as a requisite condition comes name-and-form.' Thus it has been said. And this is the way to understand how from consciousness as a requisite condition comes name-and-form. If consciousness were not to descend into the mother's womb, would name-and-form take shape in the womb?"
"If, after descending into the womb, consciousness were to depart, would name-and-form be produced for this world?"
"If the consciousness of the young boy or girl were to be cut off, would name-and-form ripen, grow, and reach maturity?"
"Thus this is a cause, this is a reason, this is an origination, this is a requisite condition for name-and-form, i.e., consciousness."
"'From name-and-form as a requisite condition comes consciousness.' Thus it has been said. And this is the way to understand how from name-and-form as a requisite condition comes consciousness. If consciousness were not to gain a foothold in name-and-form, would a coming-into-play of the origination of birth, aging, death, and stress in the future be discerned?
"Thus this is a cause, this is a reason, this is an origination, this is a requisite condition for consciousness, i.e., name-and-form.
"This is the extent to which there is birth, aging, death, passing away, and re-arising. This is the extent to which there are means of designation, expression, and delineation. This is the extent to which the sphere of discernment extends, the extent to which the cycle revolves for the manifesting (discernibility) of this world — i.e., name-and-form together with consciousness.
In Piya Tan's commentary on Dependent Arising:
In Diagram 5a, the viññāṇa (consciousness) of the looped version is actually cognitive consciousness, which comprises both “consciousness” — as the 6 sense-bases and the 6 consciousness; hence, there is no need for mention of the 6 sense-bases again. However, in the looped versions of Diagram 5b, the nāma-rūpa that feeds viññāṇa is what, in Abhidhamma, is called the bhav’aṅga, the “birth continuum.” At the moment of dying, this bhav’aṅga is the cuti,citta, “death-consciousness,” and is also the paṭisandhi,citta, “rebirth-consciousness” of the next life. The modern term for this is the existential consciousness.
So, here, two types of consciousness are described - existential consciousness or rebirth-consciousness that is the requisite condition of name-and-form, and name-and-form is the requisite condition for cognitive consciousness (eye consciousness, ear consciousness, nose consciousness, tongue consciousness, body consciousness and mind consciousness).
The Madhupindika Sutta (MN 18) has the formula "dependent on eye & forms, eye-consciousness arises; dependent on ear & sounds, ear-consciousness arises" and so on. So, that provides the connection between cognitive consciousness and the six sense-bases in different versions of the dependent origination's links.
In his commentary on Viññāṇa (Consciousness), Piya Tan wrote:
A similar description is given in the Mahā,nidāna Sutta (D 15), where it is said that if no consciousness were “to descend into a mother’s womb,” or “were to depart” after that, nāma-rūpa would not form; or, if consciousness “were to be cut off” in a young person, nāma-rūpa would not develop and mature. In simple terms, this means that our sensing the world or our sense experiences or sense stimuli are what make us, create what we are. This mutual conditioning of Viññāṇa and nāma-rūpa shows that no part of an individual should be regarded as having independent existence or selfhood. This fact is clearly shown in the stock formula found in the Mahā Punnama Sutta and elsewhere:
Whatever kind of consciousness there is, whether past, future, or present, internal or external, gross or subtle, inferior or superior, far or near — one sees all consciousnesses as they really are with right wisdom, thus: “This is not mine; this I am not; this is not my self.”It is when one knows thus, when one sees thus, that in regard to this body with its consciousness and all external signs, there is no latent tendency to I-making, to mine-making and to conceit.
Further relationship between consciousness and name-and-form can be found in the Cetana Sutta (SN 12.38):
[the Blessed One said,] "What one intends, what one arranges, and what one obsesses about: This is a support for the stationing of consciousness. There being a support, there is a landing [or: an establishing] of consciousness. When that consciousness lands and grows, there is the production of renewed becoming in the future. When there is the production of renewed becoming in the future, there is future birth, aging & death, sorrow, lamentation, pain, distress, & despair. Such is the origination of this entire mass of suffering & stress.
"If one doesn't intend and doesn't arrange, but one still obsesses [about something], this is a support for the stationing of consciousness. There being a support, there is a landing of consciousness. When that consciousness lands and grows, there is the production of renewed becoming in the future. When there is the production of renewed becoming in the future, there is future birth, aging & death, sorrow, lamentation, pain, distress, & despair. Such [too] is the origination of this entire mass of suffering & stress.
"But when one doesn't intend, arrange, or obsess [about anything], there is no support for the stationing of consciousness. There being no support, there is no landing of consciousness. When that consciousness doesn't land & grow, there is no production of renewed becoming in the future. When there is no production of renewed becoming in the future, there is no future birth, aging & death, sorrow, lamentation, pain, distress, or despair. Such is the cessation of this entire mass of suffering & stress."
Notes: The seven obsessions are: the obsession of sensual passion, the obsession of resistance, the obsession of views, the obsession of uncertainty, the obsession of conceit, the obsession of passion for becoming, and the obsession of ignorance. See AN 7.12.
So, what one obsesses over (clinging), creates the landing of consciousness for the future rebirth. That's existential consciousness. With existential consciousness as the requisite condition, comes name-and-form. But from name-and-form as the requisite condition, comes cognitive consciousness, which is the requisite condition for contact, which is the requisite condition for feeling, which is the requisite condition for craving, which is the requisite condition for clinging, (then becoming, birth, ageing and death). Clinging here then is used to create the landing for the future existential consciousness.
So, this is how the name-and-form comes about and endures.
It is also interesting that the third noble truth says that to end this cycle, craving must be ended. That cuts the cycle.
The Buddha did not teach about an impersonal reincarnated mind-stream. This idea comes from later people.
Any teachings taught by the Buddha that are interpreted to mean "reincarnation" are based in the view that a "self" or "person" is reincarnated.
If a "self" was not reincarnated then there would be no incentive to be moral.
The Pali suttas say teachings that side with morality also side with the view of "self" (MN 117).
The common neo-Buddhist view that impersonal reincarnation occurs negates the purpose and efficacy of both the higher & lower teachings.
Not viewing absolute impermanence negates Nibbana & liberation.
Not viewing self in reincarnation negates morality.