Actually after reviewing your post again you state that the parking lights work with blinkers but not when you pull the switch so I think the dimmer switch may not be the answer. It is a great suggestion because as wrench stated it gets pretty crappy on the floor mounts. But your parking lights do not wire at all through your dimmer switch and you state that they work with the blinkers. I think it may be your switch.


1946 Chevy Pickip