Noob here, first post but is far from the last

I've taken a bunch of electrical tape off of my truck on the left hand side under the airbox in a hunt to find the reasoning for one of my headlights exploding constantly.

I found many melted ground wires (white/black) and a mysterious red wire with black markings (not a stripe) running up to a quick-splice tapping into a black/red wire of the coil/igniter wire harness. the red wire comes up from the alternator, and when I took the splice out, the battery light comes on.

Does anybody know where this wire is supposed to go?

Here's the red alternator signal wire splicing in to the igniter

When I took off the fender to follow some melted wires, I also found a matching wire. I hooked the two together and the battery light stayed on. Could it be something is disconnected under the dashboard and the previous owner didn't want to deal with it?

 

Exploding headlights-cool. Annoying, but cool.
FSM shows the red wire going to 'check engine'. Probably another break somewhere, from the looks of things,
Good luck