wait a minute… worst thing in the world you can do in a moist basement is add a moisture barrier and trap more moisture in…especially if your gonna sheetrock it… insulating the floor wont do much unless there is cold air entering the basement, in which case, that should be addressed. Moisture barriers on the floor and walls in a basement is best, along with insulation on areas not below the frost line…but the ceiling is a bad idea…unles you have a vent system to control humidity… which can effect temperture…which in turn may require floor insulation… vicious cycle.
Just want to add that I find a significant amount of mold and wood destroying insect damage in sub-structures that have a moisture barrier on the ceiling of a moist basement. basement are meant to breathe. That said… insulation on the ceiling, with active ventilation in the moist basement might work fine… use purple or greenboard of course.
The electrical box your discussing is most likely a doorbell transformer. (looks like several small “plates’ if you will and is about 2.5” square). Cant have 110v going to a rainy location that we intentionly touch. The transformer steps the voltage down.