I had a problem with no backup lights on a 2000 Mountaineer, also my auto-locks did not work and by rear window defroster didn't work. I checked all the fuses and relays and everything looked to be okay. I couldn't figure it out until another member was having a problem with his rear defroster and it turned out to be a blown fuse (fuse #20 something). I knew I had checked all my fuses, but I went back and looked for that particular fuse - it was missing. Just an empty slot. I compared the slot on my 2001 EB and it had a fuse in that location. Stuck a fuse in it the Mountaineer and everything started working. The owner's manual didn't even mention those functions were related.
Also, don't rule out an issue with the neutral safety switch. Its what turns on the backup lights.