Dear friends,
I am grateful for the enthusiastic response and the helpful comments. My current vision is for an LCD mounted on the box to provide vague clues about how to solve the puzzle and open the boxes. For example, a button press might cause the following to be displayed:
** Distance: 120km**
** Time: -11d**
** Proximity: unknown**
__ Access denied__
"Access denied" because the box is still 120km away from my "magic" location, Christmas is still 11 days away, and the twin box is not detected nearby. The recipient must decipher these clues to (legitimately) get the goodies inside the box, namely the Arduino and the GPS unit!!
@chilinski: I think that's probably the kind of lock I'm looking for, but hopefully I can find one that is smaller and consumes less power? Also, what happens to those when the power is disconnected (because the battery died?)? Do they still latch?
@macegr: I thought of using a servo to move a pin, but I'm very klutzy with mechanical design of this type and feel certain that I'd make a mess of it and get the pin stuck at exactly the wrong time.
@Gordon: The idea of having to get my saw out to extract the goodies from my box worries me too. Rev 0 of my projects typically contain a bug or two! Since I am a software guy, I had thought of inventing a secret morse-like access code that one could tap in using the button, but your "magic screw" idea is pretty cool and more failsafe.
@gnu_linux: OK!
@mem: What a good idea to make some use of the mechanisms lying dormant in the pile of old CD drives I have! I'm going to have to give this serious thought! That would be awfully impressive for the box, after a month of dormancy, to suddenly whir to life and dramatically open a drawer. It would almost be like a scene from a movie!
@MikMo: I may buy that deadbolt just to play with. Thanks for the tip!
@Phil: I dug around through the forums but can't find anything terribly apropos. It think it's amusing that guys like me post one-of-a-kind questions in the "Frequently-Asked Questions" forum. If you can't find your answer in one of the 1140 topics already posted there, then by definition it isn't a FAQ! 
Another concern I'm starting to have is power. I had originally thought that I would design the box to be almost always asleep, waking for only a few seconds to read the GPS and generate the LCD report after a button press. But then I realized that while asleep, the internal timers do not work (duh!) and so I won't be able to tell if it's Christmas without hooking up some kind of real-time clock chip, which consumes power of its own. It will destroy some of the mystery of the box if the recipient has to change the batteries four or five times or plug it in or lug around a 5kg battery.
Thanks for reading my ramblings.
Mikal