A few melted spots in headlight harness

Larger wires can help reduce overall resistance in the circuit, but notice where the damage occurs.
What does that tell us?

Damage occurs where the most heat is generated. So that was either or both:
* Location where resistance to flow was higher.
* Place where heat couldn't dissipate so it got hotter.

The connections are almost always the location of highest resistance.

Heat damage also is cumulative on the terminals and the wire.
The insulation gets worse and maybe more important, surface contaminants burn and oxidatiion build up is worse.
Clean the terminals and crimps with some deoxit or similar. Tighten the crimps and loops if needed, and/or replace if bad.

I think if a car never got the newer 6014 headlamps, there would have been less headlight circuit issues. But after 10 years most cars have had the headlights replaced, and what was available was rarely the older 6012s. I had the circuit breakers trip off on my a-bodies in the mid 1980s. Car was only 15 years old.