Need a little help with my 76.  My high beams go off.  Switch back to lows and have lights.  I have had the highs to go off and come back on and go off again, back on, back off and stay off until I go back to lows.  I have halogen lights.  The lows and dash lights do not go off.  I replaced the dimmer switch and thought I had solved the problem but not!  Sometimes you can drive for quite awhile before they act up.  Help me out Vette guys.

David, are BOTH of the hi-beams going off at the same time? My first suggestion would have been the dimmer switch, but you covered that already.
I would suspect a ground problem with the hi-beams, or a break in the wiring between the dimmer switch and the bulbs.
If you turn the highs on, and reach under there and wiggle the connector on the bulbs, do they blink/flicker?
You may need to wiggle every connector in the headlight harness to determine if that is the problem.
Another area to check would be the firewall pass-thru connector, where the fuse box connects to the forward harness. Many times, this connector will have corrosion on the terminals, and if you put a high load on the connnection, such as hi-beams, it will fail. This can be checked by removing the small bolt(5/16") in the center of the connector on the engine side of the firewall, and unplugging the connector to view the terminals inside.

The high beam circuit/terminal is #14 in the connector, and has light green wires in it. This is probably the source of your winky-blinky problem, but be sure to check the grounds(black wire) on the headlights first.

Thermal circuit breaker is what I reckon the problem is.  With the Halogens (all 4 of them) in circuit you are drawing way too much current for the poor little headlight breaker.  Don't know where it is on a 76, but I would say that's why the lights go out and come back on.

I thought of that, too, but...the low beams are not going off, nor are the other lights. The breaker is built into the light switch itself.
Normally, when the breaker trips, all of the lights will go off...tail, dash, head...

David, when you replaced the dimmer, did that help at all? It sounds like you thought that it was fixed, but then they went off again, but it took longer for it to happen? If so then the bad connection could be at the dimmer switch itself. Just an idea..