80’s/90’s Psychological Thriller with Schizophrenic Villian

I watched this movie with my dad as a kid but cannot find out what it is called. Google and whatismymovie have not helped.

It is a possibly 80’s/90’s psychological crime thriller centered around a villian (possibily stalker, killer or kidknapper) whose identity is not revealed until the end of the movie – He is only seen by the his eyes reflected on a rear view mirror or hands on steering wheel (I recall a driving scene).

The villian talks to himself (possibly to a dead mom too) and sings (I think it was she’ll be coming round the mountain or something similar).

At the end of the movie the villian is revealed to one of the main characters. I want to say he was a doctor but I’m not too sure about that.

Any help would be greatly appreciated as I’m trying to think back 20 years ago to when I saw the movie.