"All cittas and cetasikas are collectively classified as name. The life force or life principle of name is called jivitindriya. All cittas and cetasikas can function actively because of this life force or principle. If this jivitindriya is absent, mind cannot function at all. In short it is jivitindriya that prompts cittas and cetasika to continue arising according to kamma. There is also a living part called rupa jivitindriya in the material element. The vital force of mind and matter therefore termed nama jivitindriya and rupa jivintindriya respectively. These two in combination forms the “life” of a being. Apart from this two, there is no such thing as eternal soul, or ego. There is no attá (self) at all"
~ Cited from: Jivitendriya, one of the seven universal mental factors
As far as I understand, nothing goes from one life to the next. There is no soul. It's just the mind stream continues with the help of the universal mental factor, Jivitindriya (Nama Jivitindriya). If the flow of the Rupa Jivitindriya stops we call it "death". After the last consciousness (cuti citta) of one's life, the first consciousness of the next life (patisandhi citta) will arise. There is no gap between these cittas which connect two lives. Consciousness does not travel across the space from one place to another at rebirth. The originated consciousness/mind dissolves at the same place.
"Suffering exists, but no sufferer can be found. Actions exist, but no doer of actions is there. Nirvana exists, but no one who enters it. The Path exists, but no traveler can be seen."
"There is no doer of a deed
Or one who reaps the deed’s result;
Phenomena alone flow on—
No other view than this is right.
And so, while kamma and result
Thus causally maintain their round,
As seed and tree succeed in turn,
No first beginning can be shown.
Nor in the future round of births
Can they be shown not to occur:
Sectarians, not knowing this,
Have failed to gain self-mastery.
They assume a being, see it as
Eternal or annihilated.
Adopt the sixty-two wrong views,
Each contradicting one another.
The stream of craving bears them on
Caught in the meshes of their views:
And as the stream thus bears them on
They are not freed from suffering.
A monk, disciple of the Buddha,
With direct knowledge of this fact
Can penetrate this deep and subtle
There is no kamma in result,
Nor does result exist in kamma;
Though they are void of one another,
There is no fruit without the kamma.
As fire does not exist inside
The sun, a gem, cow-dung, nor yet
Outside them, but is brought to be
By means of its component parts,
So neither can result be found
Within the kamma, nor without;
Nor does the kamma still persist
[In the result it has produced].
The kamma of its fruit is void;
No fruit exists yet in the kamma;
And still the fruit is born from it,
Wholly depending on the kamma.
For here there is no Brahmá God,
Creator of the round of births,
Phenomena alone flow on—
Cause and component their condition.
~ Cited from Path to Purification (English translation of Visuddhimagga)
“Cetanaham bhikkawe kamman wadami."
"Intention, I tell you, is kamma."
~ Cited from: Nibbedhika Sutta, Anguttara Nikaya, Tipitaka
Cetana (Intention) is a universal mental factor which can be seen in every consciousness/mind. But not all Cetana becomes kamma. Cetana which can be seen in 12 Unwholesome Consciousness (Akusala Citta) and 17 Mundane Wholesome Consciousness (Laukika Kusala Citta) become kamma.