It doesn't really have an effect on the circuit.
You are also correct on the three switches. One shorts the two leads directly and the other two short the leads but use a capacitor to create a signal. The rate of discharge of the caps determines the behavior interpreted by the garage door base.
What about your code? How long are you powering the transistor on/off for as this will affect the action taken as a button press.Are the switches momentary close or momentary open (or a mixture of both)Do you need a resistor in the emitter or collector line to limit current through the transistor?
Again I'm just as interested in why this doesn't work as a solution (i.e. just use a relay).
PS A relay would be easier. lol...