Once an electrical harness has been tugged and ripped on (by some thief), there's no telling. The nice thing is, it's all fixable
Like Arctic was saying, burned connections are pretty typical evidence of high resistance/high current draw, caused by a loose connections. I'm surprised it didn't blow a fuse.
If it were me, I'd revisit the harness around the area that had been abused by thieves, repaired by a shop maybe, closely examine the wires, replace any suspect sections with new wire (solder and shrink wrap only).
Equally as important as the +pos wire, are the grounds. Electrons won't flow if the path is blocked by a bad ground. When electrons try to jump the gap in path, the white powdery corrosion that acts as a blockage, they arc (think arc welder) or jump, and leave burn marks as evidence.
Like yours, my van is getting pretty 'long in the tooth' as well. Bad grounds, and connectors that are starting to get corroded will drive you nuts chasing things that 'sometimes work'. Staying ahead of this, every chance I get, every time I touch something electrical, I closely examine both the connector, and the grounding means. I remove the ground wire, the lug, whatever grounding means that device uses, and sand the contact areas with 100gt paper or hit it with my grinder. In fact, I just did this on my fuel selector valve 2 weeks ago.