The wiring on old bikes can be a real pain. I was/am in the same situation as you, burned wires, wires soldered together badly, nonsense splicing etc.
But on the other hand, when fixing it, it's nice to know that what you are doing only makes the bike in a better condition than it was before. If you are not comfortable with wiring it might be an idea to look for a new harness, price depending.
Get heatshrink in various sizes, connectors and spare wire, tin and a soldering iron, it'll be worth it if you're going ahead.
Good luck on the project!