Very common problem on Ford. I don't recall many problems with GM, but it sounds like the headlight switch.
My 77 Mercury used to do this constantly until the switch was replaced, and my 78 Thunderbird that I restored..., the switch actually caught on fire.
Working on the police cars in my past life, if you have continual problems, add a 30 amp fog lamp relay. This way you can mount the relay somewhere, either side of the radiator, and use the lead from the headlight switch as the input to the relay. So this way when you turn the headlights on it energizes the relay, and the high amp pass through, is what energizes the lights.
The reason you use the fog lamp relay, is because it's designed to carry the 30 amps and stay on for long duration. Most other relays are designed for short duration, which means they can't handle the amp load for long periods of time and they burn up.
If you have problems of the high beams doing the same thing, then do the same thing. Run the high beams through a relay.