In situations like this, it's probably easiest to just tier the logic. Have your func_button trigger a logic_relay everytime it's activated....like open_doors_relay and close_doors_relay. Then you can worry about making the button 'just' move down when the doors should be closing...which would entail probably a knife switch rotation. I think there's a model called "prison switch", which is probably what you're looking for.

Anyway, back on track. Push the button, button triggers open_door_relay, open_door_relay outputs to X number of doors to open and also causes the switch to rotate. Make sure to time how long the switch rotation takes, so that you can ignore user input until the doors are fully opened and the switch has fully rotated. After that, repeat the process in reverse for the close_doors_relay.

If it's the rotation you're worried about, it kinda depends on if you're using a model switch, or a brush switch. Either way, though, you'll just have to parent the moving part of the switch to a rotate function. On the flip side, func_buttons inherently slide when pressed, so that might be another solution.