Start with the connections at the bulbs, first. Make sure they are clean, and no corrosion on the terminals. Then pull the carpet back and check the conn.s at the hi-beam switch. If all else fails, you may have a sick headlight switch. Make sure all the grounds are good on the bulb connectors. Hopefully, you have a wiring diagram for you car, which will help to locate the grounds. If not, I'm sure some other C3VR member will have one. Good Luck! Hope this helps some. My money's on the hi-beam switch, since it sounds like BOTH hi-beams are flickering. my $.02Adams' Apple38396.6556944444

Here is another possibility.  Do you have Halagon headlamps?  They draw more power than the original incandescent lamps draw.  As a result, the circuit breaker in the headlight switch trips and cuts off the lights.  As the breaker cools, they turn back on.  I have seen this several times on 70s GMs.  See if the power coming out of the headlight switch goes away when this happens.  If so, the breaker is the problem.

Sometimes the breaker is just worn, and a new headlight switch can correct the problem.  Other times, the lights just draw too much to for the switch circuit breaker to handle.  Then you have two choices.  1. Put standard bulbs back in. 2. Rewire the lights with circuit breakers to prevent the overload at the switch.

I have another thread with the diagram of how to make the change.

That's exactly what mine was doing last summer. I replaced the high beam floor switch and problem solved. I think it ranks as the cheapest repair/fix I've had to do..