Mystery solved!
Before the trigger fell out of my AMT Back Up I had taken the riops off so I could look inside (I hoped) and see why that could happen.
OK, the trigger is kept from coming out by the pin I mentioned that slides into the hole in the rearward most extension of the trigger, a small narrow tap that projects backwards out of the trigger to the rear on the RH side, which slides into a slot in the frame. That slot is exposed on the outside of the frame under the grip.
There is a trigger bar that slides forward and back on the outside of the frame under the grip, and at it's forward end is a projection with a small pin. That pin slides into the small hole at the back RH rear of the trigger, and holds the trigger from coming out.
What keeps the trigger bar in so that pin will stay engaged is,,,you guessed it, The grip. But, the screw that holds the grip in place is at the rearward edge, the front edge has a lip that slides just barely under a tiny ledge in the front edge of the frame cutout.
So if you take the grip off and put it back on without that lip being under the ledge there is really very little but the rigidity of the plastic grip to hold the trigger bar in so that pin can keep the trigger in. Also, there is a return spring behind the trigger itself that will "help" the trigger pop out if the bar slips to the right.
Simple really, and I should have guessed there had to be more than one small screw at the rear edge of the grip to keep it secure.