Mystery is [finally] solved.

I called in the pros (i.e., the fabled Maytag repairman) and he opened the freezer door and knew instantly what the problem was and how to fix it.

There is no drain on this freezer. The defrost/dehumidify functions are handled by a small ventilation fan that cycles air from the freezer into the refrigerator side and returns it. This carries away the excess moisture before it ever condenses on the walls of the freezer, and it brings cold air into the refrigerator, the amount regulated by a sliding lever to keep it at the correct temperature.

The repair took 45 minutes with a two man crew who drove 50 miles from Guadalajara, and cost $2,000. Fortunately that was $2,000 pesos, not dollars. Figure $89 USD, of which $58 was for parts. Gotta love Mexico.

tanstaafl.