Air conditioning

That door uses either a motor or a vacuum actuator to pull it open/closed. From your description you have a vacuum leak in one of the control lines to the actuator. When you step on the gas the vacuum drops off and the door moves. It's also possible that the door is broken. To get to the actuator you remove the right hand duct cover, the dash braces and the lower air duct. The actuator is behind the duct. If it's a vacuum type you can test for a leak in the lines by selecting hot/cold while the engine is running and check for vacuum at both lines as you move the control. One should get full vacuum while the other gets none and that should reverse when you move the control. If you have vacuum on both, step on the gas and see if one drops. If it does the issue is in the lines between the actuator and the control head. If it stays steady the fault is in the actuator or the door itself. That you can check by removing the actuator and moving the door shaft.