63 Valiant Wiring Harness

Yes, when I got my '63 Signet 'vert it too had the under dash wires fried badly - melted into each other. I too wondered how it hadn't caught fire. I wouldn't have know except that I stuck my noggin up there because there were no lights - GEEEES! - I freaked out.
Like the previous poster, i replaced them all one at a time and soldered in wires from an Aussie Valiant harness. Not all colours were correct but most were the same.

It took a loooong time and isn't a fun job.

I would try to buy a good harness if poss and replace it, holus bolus. The only drawback is that wiring is VERY old so the donor harness would need to be in good condition.
Good luck and let's know how you go.