[RustyPile]

That orange wire along with the white one is the dome and courtesy light circuit. Orange being the feed, white the ground. The orange wire is always hot and goes to the brake light switch and all the bulbs. The white wire on the brake light switch goes to the turn signal switch. The other white wire on the courtesy lights goes to the headlight switch and door switches. These 2 white wires are not tied together, they are totally different circuits. Twisting the headlight switch knob activates the dome ground (white wire) and turns on the light. Opening a door switches the white wire to ground and turns on those lights.

Why the headlight plug overheated is anybody's guess.. Probably because items connected to it shouldn't be. The first sentence of your first post explains a lot of things..

The first item in your electrical toolbox should be a proper wiring diagram. If you don't have one, it's available as a free download at the top of this forum.