The early headlight switches incorporated a circuit breaker. It could be that the switch is defective.

This is unrelated to the problem with the lights but you indicated that you have a 12 volt system with a 6 volt coil.
A correct 12 volt system should have a ballast resistor and use a 12 volt coil that is stamped with "for use with an external resistor".
A 55 up car or 55.2 truck will have the correct coil.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine