I made an assumption about the cause based on the symptoms you posted. You can verify the cause by taking voltage drop tests when the symptoms are active.
With the headlamps on high beam, maximum current passes through the integrated circuit breaker. GM had a 'problem' with their headlamp switches in that the switches were stressed to their limit. If you upgraded your headlamps so they pull more current than the originals, the circuit breakers would cycle from overload. In some cases, the headlamps would cycle even under normal circumstances. The solution in such cases is to install a high beam relay.