I have access to every resistor, capacitor, PIC and known.
And again, would've been handy to know that in the first place.
Single button at the shooter end to do the triggering...
Brains (PIC), 1 push button, relays (to do the door opener button pushing), etc, at the target end to do the work...
Start with target down...push button is pushed providing the input to the PIC that the target is down...
Shooter pushes button...
PIC sees the button pushed, checks the lever switch to see if it's closed, looks at the DIP switches attached to it for a delay (unless you want a random time, then program it that way), waits for the delay (if any), then actuates the relay which connects the door opener button. (or if the switch is open immediately actuates the relay...which is the case below)
Door opener swings the target up, the push button that was pushed is now not pushed, therefore, if the target isn't down, it must be up.
Shooter pushes button again...
PIC sees the button pushed, checks the lever switch to see if it's closed. If it's not, immediately actuates the relay to swing the target down.
Door opener swings the target down, same lever switch gets engaged, PIC goes back into a holding pattern waiting for something else to happen.
And I think a garage door opener is overkill unless the targets are really heavy.
Could likely go out to the local junkyard and get a power window motor or wiper motor for $10-$20, but would have to add a few things like limit switches and probably a couple of relays.