Burnt headlight socket

When I picked up my 87 NA GLL I noticed the previous owner had installed a different headlamp socket than the factory sockets, and it was giving me a dead headlight.

Some searching pointed me at the headlamp switch, which I cleaned up with sandpaper and packed with a little grease to keep from corroding again. That fixed my dead headlight, but the headlights were remarkably dim. The fog lights are brighter than my headlights.

I started poking around for some answers with my multimeter one night and noticed my bulb was fused to the already replaced socket. Kept yanking and the bulb came off, but left a piece behind. Pulled that pin out and the ground pin had melted plastic to the bulb.

I'm going to pull the alternator and have it checked but I think I have a ground issue. I know the GLLs ground through the headlight sensor but where does that sensor ground to the body?