Aha! I figured out a way to fix the light button. It's working pretty darn good again.

In case anyone is interested, I did it thanks to an old credit card. First, I used the card to open the remote (sliding the card around the edges of the remote to release the clips.) Then, using scissors, I cut some tiny pieces of rectangular plastic from the credit card. I was able to slide one of the plastic slivers in between the remote's circuit board and the broken light button. The key is that the sliver had to be cut precisely so that it will fit snug in between the button and the circuit board, thus ensuring that the sliver acts as a makeshift anchor to hold the button in place.

It took a few tries to get it just right . . . but now the button works like new again. The button has that nice "clicky" feel to it like a new remote does.

It's fun to keep these loyal old URC remotes working :)