And in additon, replace the main wires from the battery, regardless of appearance:
- the black to the starter
- The red to the main breaker
- The main grounding wire. Here you need to also make sure the contact with the frame is good (use a star washer to penetrate paint/oil/rust).
After that, with basic electric skills/knowledge and a VOM measure voltage drops. It is not complicated, and that bike has very simple wiring lay-out.
Note that I'm no electrical enigneer, but I completely re-wired my old '88XL and partly my current bike. It's just a matter of using common sense, a VOM, and using the wiring diagrams (following colours).
I found my old diagram - for '86-'90 XL - but should be sufficient for this one as well (I can email you a larger version).