"I thought there was an automatic switch to the battery bus and then load shedding was activated. That would give you some power for a while."
The battery provides power to only certain aircraft systems, Onan. Those that use DC power can work directly off the battery, those that require AC power require a Static Inverter which converts DC to AC. ATC is AC-powered, but is not normally one of the systems powered by the Static Inverter (for power conservation reasons).
"Also, doesn't the third horizon have to have it's own independent 30 minute power supply?"
You're probably thinking of newer generation aircraft. The design of the 767 is quite old. These NG aircraft have low power LCD Integrated Standby Flight Displays... and the dedicated battery can last up to 150 minutes (depending on battery charge). The 737NG, some Airbusses and the 747-400ER have these.
Regards.
Q.