I had a similar occurrence on my '59. The head lights on one side would tune off at random times. The culprit was a loose fitting connector behind the headlight bucket; it would vibrate loose just enough to interrupt the circuit. Hope this helps.

Oldbolter
1959 Apache 3800 dually flat bed/dump with 261
1956 3800 dually flat bed/dump with 235
1957 3600 flat bed, 350 engine, 700R4, PS, disc brakes, 14 bolt rear with 4.11 gears