As far as I remember, there 'should exist' an exact etale realization functor from the category of mixed motivic sheaves (over a base scheme $S$) to the category of perverse $l$-adic sheaves over $S$. However, I was not able to find this conjecture in the literature. I would be deeply grateful for any references or details and comments here!

Upd. I would like to understand here the interplay between the residue fields of a scheme and their separable closures.

It seems that I know most of the main reference on the subject; yet I cannot find a very precise answer to my question (possibly it's still there but is difficult to see).