
I have a crate in the back of my car for the dogs and attend agility shows so the tailgate is often open. My alarm doesn't go off but the courtesy light stays on and runs the battery down. A friend showed me how to get round this - I have to push in the locking bar on the tailgate lock to fool the car into thinking the tailgate is locked shut and I can then use the fob to lock the car with the tailgate up. When I unlock the rest of the car I have to manually push the handle in on the tailgate and as one would to open the gate if it was closed but the car was unlocked.
I have wind down windows in the back of the car and it is these I leave wound down a little rather than the front electric windows. Some cars have a switch that overides the lights in the cargo area but mine doesn't have one so have to resort to the above method which does work well. Might be worth seeing if yours would do the same.