As I recall on my ol'59 the outside lights were dual filament (hi/lo) and the inside lights were single filament (high only). They are 2 completely independant circuits controlled by the dimmer switch.

Lets say the new wiring harness came with a 15 amp breaker for headlights that is wired through the headlight switch then to the dimmer switch. On low beam, everything is fine. But when the highs are switched on the circuit pulls (lets say) 18 amps. It works for a few seconds, then "poof" no lights. The problem appears to be between the dimmer switch and the headlights as the low beams work fine, but actually the problem is way back behind the dimmer switch. That's why I'm saying the glitch could be anywhere in the circuit.

I was also curious if he replaced the light switch as it may have a thermal protection that is not rated for that much load.