Have you tried confirming the functions of the wires using either a multimeter or a test light? For example, does the wire that should be White/Orange only have voltage to it with the switch in the "On" position? Based on your description, it sounds like it will have power all the time. The next thing to check would be to pull the rear wiper relay from the rear auxiliary junction box and check for ground to terminal 2 which should have a light green wire to it. It would correspond to either relay pin 86 or 85. If you have ground to that terminal when the rear wiper switch is in On and Off, then the GEM is telling the relay to close all the time to power the rear wiper. If the ground seems to be switched appropriately (Ground with the switch in "On" and open circuit when the switch is "Off") the relay is the likely culprit.

If the signal from the GEM to the relay is grounded all the time, before condemning the GEM you'll need to confirm the signals from the switch to the GEM are correct.

Also, what is the build date of your Explorer? How many wires did your old motor have, and how many does the new have? The "Early build" 2002 Explorers apparently have a 3 wire wiper motor while the "Late build" units have a 4-wire microprocessor controlled motor assembly.

-Rod