The film about the car that chased people was "The Car" from 1977 starring James Brolin. It was a Lincoln Mk3 modified by George Barris.
Haven't seen Deathproof yet, but that's sort of what I was thinking of. Generally his style of dialogue in all his films esp. Reservoir Dogs is very sharp and realistic.
I was thinking of the Charger from Bullitt. That's the archetypal sinister car.