I covered the 777 RAT a few pages ago. It deploys automatically after both AC transfer busses remain unpowered for 15 seconds. Can be deployed at the push of a button, yes.
Fuel exhaustion is one scenario that would trigger auto RAT deployment, that is to say a loss of AC power due to both engines spinning down and no APU start. Not a 777 driver, mind you, but you'll find the information above to be accurate from a maintenance engineer's point of view.