I'm guessing defective switch. There is only one wire that runs from the headlight switch to the tail light. If it works in the parking light position, it should be OK for the headlights on position. Try shooting the switch with some contact cleaner (Remember that stuff from when we had mechanical channel changers on TVs? You can still buy it.) and then operate the switch back and forth a bunch of times between the parking and headlight positions. If that doesn't fix it replace the switch.
'57 GMC 102, Original 347 V8, HydraMatic, 3.08 rear gear, added A/C, disk front brakes, HEI, AFB carb, '98 Honda Black Currant paint. T-boned and totaled 10/12
'52 GMC 152 Stake Bed, Original 228, SM420, added A/C, HEI, disk front brakes, '67 Chev 3.55 rear gear. Gets used as a real truck.
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