You are doing great. I think more mechanics are scared of eletrical gremlins
than all the other problems combined.
My guess is bad switch or short inside your dash, maybe the same one that
fried your other wire. Take off the lower dash panel to make getting to wires
in the dash easier. Pull out one seat and put a carpet or something in there
so you can lie comfortably on your back and look up at the wiring.
Changing the switch is tricky because of all the connections. Take good pictures
of it before doing it. Maybe someone has a known good one to loan you. The
simplest answer would be a short inside the switch is causing the headlights
to cycle up and down.
I have connected a 5 amp fuse between the negative terminal and main ground
when initially debugging my car. That way the 5 amper fries before taking your
wiring with it. You can't crank your starter with this set up, but you can test all the
smaller stuff.
When you get it all figured out, come over to my house and help me figure out
why my red car won't start anymore.
John