I was thinkin', and agree, the rectifier came to mind first.
That's where the wire burned to, check that first maybe.
A voltmeter at the local hardware store, 10 dollars or less.
You're blind without one.
No meter, I'd disconnect all but the start and run wiring,
reconnect the rectifier, the lights, the horn, one at a time
while running till you start smoking wires again.
Advanced shade tree mechanics right there
Good luck keep us posted, I know I'm interested.