So, my third fl. Shower pours water once or twice a month onto the ceiling below, but not during the shower- usually 1-3 hours later? The tiled shower was installed about 15 years ago, I think with a copper pan.
What is going on? Where is this water resting and why does it tip out in a gush (one to two bucketsful). Do I have to break up the tiles or should I cut the ceiling below first?

I think I would cut the ceiling to see where the source is. It's as much a mystery to me as it is to you. Look for moisture around the drain and trap. If you don't find any there check the outside of the pan to see if it's leaking from the tiles and running behind the pan. Let me know what you find. Good luck. Tom