When I use the high beam on my Z28 it works fine for about 10 minutes, then the lights goes nuts... and starts to turns off and on..I can also hear the relay click.. It stops when I turn off the high beam and if I turn it on again it works again for a couple of minutes.
The funny thing is that my friends Iroc has the same problem I think we both have H4 bulbs.

Could it be a relay failure?

 

If you have installed relays to control the head lights and you also have factory fog lights, that may be the problem. The factory fog light relay coil grounds through the high beam filaments (turns off the fog lights when the high beams are turned on), so replacing the high beam filaments with a relay coil puts too much resistance in the circuit - if this is the case, add a small bulb in parallel with the coil of the relay that you added for the head lights, or disconnect the fog light relay from the circuit - cut the light green wire & ground the end connecting to the fog light relay coil.