The following is taken from the subtitles (grammatical errors appear in the film) in the 1979 movie Wise Blood:
Hazel Motes: I only follered her to say I wasn't beholden to none of her fast eye like she give me back there.
Preacher's Daughter: What do you mean? I never looked at you with no fast eye. I only watched you tearin' up that tract.
Since she seems offended, my first thought was that "fast eye" means "looking at with physical attraction."