Jon beat me to the punch. Do Jon's check above first. If all is okay then proceed with below.
So the other terminals on the light switch are okay?
The melting insulator is caused by overcurrent.
The current flow pathway is:
Ground (near headlight)
Headlight socket (in)
Headlight bulb filament (low or high beam)
Head light socket (out)
Terminal strip (in) (inner fender)
Terminal strip (out)
Dimmer switch (in) (floorboard or toeboard)
Dimmer switch (out)
Light switch (dash)
As you can see, there are multiple connections (screws or wire connectors) in the current pathway.
If any of the connections are not clean (free of corrosion etc.), they cause a resistance to the current.
The more resistance, the higher the current, the more heat generated.
This is typical of 70+ year old wiring.
It's not that the wires of the wiring is bad, it's the connections.
I clean connections by using a deoxidizer (Deoxit) sold by CAI Laboratories.
There are other contact cleaners. Some are okay. Some are horrible.
DO NOT use penetrating fluid such made by WD-40, Kroil, Blaster etc.
This fluid is made to penetrate rust. It can ruin (or very hard to clean) electrical connections.
Last edited by buoymaker; 04/06/2022 2:42 PM.