Electrical issues.

OP's car is a '64 Dart. '64 Darts did not come with parking lamps wired to remain lit with headlamps; that was limited to Barracudas til '68 when it spread to all cars. This is all plain facts; no guesses or assumptions required. The problem at hand is complicated enough without introducing spurious variables.
All you had to do was say that in the first place.

All of which is irrelevant since Del figured out the most likely source of the problem faster than either of us.
I should have stuck with post 11, LOL.