In literary criticism, stream of consciousness is a narrative mode that seeks to portray an individual’s point of view by giving the written equivalent of the character’s thought processes, either in a loose interior monologue, or in connection to his or her actions….(wiki)
Fluvius conscientia
i hope i could help .
Narratio fluens ex cogitationibus et actis narratoris.
I’d suggest making the Latin say ” to set forth that which comes into the mind of the character” ~
Narrare quod in mentem actoris venit.