I finally(hopefully)fixed mine last week. I read a bunch of stuff around this forum and thank you all for your prior information. I will add my info and maybe someone else can gain from it. The saga:
2001 Sport Trac 4x4. About 3 years ago the 4wd would not engage during the winter. No 4whi or 4wlo lights flashing after startup and no click from the right front corner when using the switch. It would start working again in the late spring, just in time for me to pull my boat trailer.?????? This last fall it quit working in October. After Christmas, I put it in the garage and pulled up the right front seat plastic door strip, the lower right vertical plastic molding under the glove box, found the 4x5" black plastic box containing the shift module, unscrewed it, disconnected the two electrical plugs, and took the piece in the house for two days. Reinstalled with small amounts of dielectric grease on all the contacts and many plug in and plug out cycles-no help.
Took the rig to Sears for a tire rotation. While it was in the air, we tapped on the shift motor with a small hammer, put contact grease in the plug underneath going to the motor, cycled several plug ins and outs-no help.
Next, I stopped at the local Ford dealer and talked with a maintenance tech. After my story he said I could still check the circuit continuity with a volt meter, as the power and ground circuits good be bad. All I got out of that conversation was that the ground is the biggest black wire of the bunch, and that with good circuits, the system not working when cold probably means a faulty shift module.
I held my breath and ordered the shift control module from Silverstate Ford, Ford part #1L5Z-7E453-AC. You can Google it for a picture. $161 plus shipping = $183. When it arrived it had the same number as the original part in my Sport Trac -#1L54-7H417-AC. They explained that the original was an engineering number and that the replacement was a part number. Go figure. The old one had a date code of 00301, which I believe is the third day of 2001. The new "part" had a date code of 13308. Middle of May 08. Hopefully, they learned something in 7 years.
When I installed the new part, I didn't disconnect the battery. I heard to do that somewhere, but the black plug on top had the biggest black wire in it(ground), so I connected it first followed by the lower gray plug. Started the beast up and all worked fine. I lost the 5 to 1 bet I had with myself that everything would work out on the first try. It just never happens. I drove it around for about 20 mins. to warm it up and shifting to 4wd several times. Just like new. Parked it outside.
The next morning I started it and drove to the gas station. 18 below zero. Shifted to 4wd with no problem.
A while back I had an Apple laptop computer that stopped booting up the way it was supposed to, and the problem was generally agreed upon that picking it up by the front edge caused a flex in the lower panel which in turn caused hairline fractures in the logic board solder points that was fixed to that panel. There was even a unofficial fix around to use a soldering iron to remelt certain suspected solder points on an out of warranty logic board-and it worked. I am now wondering if the old 4x4 control module in my ST could have had fractured solder contacts from years of bouncing around. Or it could have just been a short of some kind. Who knows? It works for now and that is my story. Hope it helps somebody.