The RAT on the 767 does not supply hydraulics for the HMG. If the RAT has deployed the hydraulic fluid is routed via an isolation check valve which ensures that the output is used for primary flight controls only.
This will be:-
i/b ailerons
spoilers 3,4.,8,9,10
elevators
rudder
It will also supply the centre a/p servos, left Yaw damper primary stab trim and elevator feel.
If the HMG was also supplied it would over load the RAT and not enough power would be available for flight controls.
Conditions for deployment are a/c in the air, 80+kts airspeed and both engines less than 50% N3
There is also a priority valve in the circuit of the A320/1 which reduces hydraulic output to the emergency generator and slats if hydraulic pressure is low or demand is high. Not sure what effect this would have if the electrical power was lost due to a dual engine failure. Perhaps a question for the next sim check?!!
Airbus deployment conditions a/c in the air, 100+kts airspeed and both main ac busses failed.
Both a/c types are able to deploy the RAT manually from the hot batt bus