My truck did crazy things like this when we got it home. Couldn't see burned wires from afar but it wasn't long after I found this forum that I saw many talk about relaying the headlight and running light circuit.
I did that when I had my dash all apart and although I didn't have melted connectors I did have a chunk of wires off the headlight switch melted together enough that it looked like a melting pot of crayons with new colors
Also got to watch out for previous owners that have tapped into the wiring for the radio which you can get to with it out. I had tons of crap taped and tied to these circuits and found another clump of wires melted near their.
It was so bad on mine that things would pulsate through the gages, etc. Headlight switch appeared to have multiple positions, one time I came out to the lights being on, and even wrong for the position of the switch
I relayed things long ago with a new switch for the hell of it, and replaced the whole wiring harness with one from the junkyard because I was sick of all the little wires that were tapped into and meleted together. It was haunted.
Also watch out for people and the way they wire aftermarket brake controllers and wiring looms near the rear lights. I had a big crimped exposed mess there as well that led to things happening when going down the road.
