What is being asked about in the question is from Vipassana Dhura, which is 16 stages of insight from the Visuddhimagga, written by the commentator Buddhaghosa in 430 CE in Sri Lanka.
The sequence of the 16 stages of Vipassana Dhura is not something the Buddha taught & can be confusing because terms used in Vipassana Dhura that indicate a beginning stage of insight- such as 'nibbida' - the Buddha used as the final stage of insight (eg. SN 12.23 - 'disenchantment'). This can make discussions about Vipassana Dhura difficult.
That said, some degree of 'nibidda' (disenchantment with worldly things) is required at the beginning of the path. Therefore, the stages in Vipassana Dhura do have some validity.
The teachings attributed to the Buddha describe the following kind of 'equinimity' (which is called 'Sense Restraint') before the arising of the path:
On seeing a form with the eye, he doesn't grasp at any theme or details by which — if he were to dwell without restraint over the
faculty of the eye — evil, unskillful qualities such as greed or
distress might assail him. On hearing a sound with the ear... On
smelling an aroma with the nose... On tasting a flavor with the
tongue... On touching a tactile sensation with the body... On
cognizing an idea with the intellect, he doesn't grasp at any theme or
details by which — if he were to dwell without restraint over the
faculty of the intellect — evil, unskillful qualities such as greed or
distress might assail him. Endowed with this noble restraint over the
sense faculties, he is inwardly sensitive to the pleasure of being
This 'equinimity' of not grasping at 'themes', when well developed, can become a kind of (deluded) liberation, described in the scriptures (MN 43 called 'theme-less awareness-release').
This 'equinimity' can be a state of delusion because the mind, being accustomed to the feeling of liberation via 'non-judging' or 'non-discrimination', does not discern the characteristics & cause-&-effect realities of many things.
This kind of 'equinimity' many Hindu, Mahayana & Zen traditions call 'advaita' or 'non-duality'. It is a delusion because the mind believes 'non-thinking' & 'non-discrimination' is liberation. Thus, the mind clings to 'non-thinking'; not clearly seeing thinking (sankhara khandha) is also 'not-self'.
Even some Theravada Sri Lankans, such as Katukurunde Nyanananda, give the impression of this delusion, as they give the impression they believe the ending of thinking ('sankhara') is Nibbana.
It should be noted this 'equinimity' is not the equinimity of the 4th jhana because the stream-enterer (1st path) has not reached the 4th jhana.