Dave,
I think Bill is on the right track.
This is an educated guess....The root cause of this may just be related to the headlight problem because that is what failed. It seems unlikely that you have unrelated electrical failures at the same time both involving the lighting circuits.
The headlight/exterior light wiring, or as Bill mentioned possibly the electrical bay breaker, could have had water in it causing leakage to ground. This current leakage provided enough drop in voltage that it activated the electronic buzzer by putting the buzzer circuit in an unstable condition. When you turned the turn signals on and added that load it could have dropped below the voltage needed to activate the buzzer at all.
When the headlights quit, I suspect that the buzzer stopped also, because either the voltages would have returned to normal or no voltage would have been supplied to the buzzer because the turn signals were on the same circuit. The breaker for the headlights opened the circuit to protect it and that should have eliminated all of the overcurrent/low voltage conditions.
Water would be the most likely source especially if it was raining or if you recently washed the coach. Other sources could be a near shorted wire due to a misplaced single strand of copper, or a carbon trail between contacts in a socket from arcing due to a loose connection. Given the light breaker reset itself after sitting, it would seem that the cause is most likely water related and the source dried out. Hope this helps....