Lots of ideas.
You'll need to check them. A visual check is a good way to start.
A little background. The headlight switch had a 15 amp circuit breaker in it. It resets itself when cool.
The breaker is only for the headlights. The parking lights get power from through the fuse box.
Your car originally was supplied with 6012 sealed beam headlights. 6014 headlights were the typical replacement but drew more current on both low and high beam. This did the wiring no favors as it was only 16 and 18 ga (hence the 15 amp breaker). Some halogen sealed beam replacements draw more current, other draw less on low beam but more on high. Look at the markings on the lens and we can tell you what the lamps are if its not obvious.
Common places to find damage are at:
the headlight sockets themselves.
View attachment 1715731144
the dimmer switch connector
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the headlight switch connector
Dana's Dart
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My 67 Baccaruda
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Some other possibilities are:
Wires chaffing against edsges of sheet metal. This can happen most easily at the back of the headlight buckets causing a short.
Ground wire issue. Ground wires for the headlamps gets screwed to the front panel the radiator mounts to.
