Read your other thread. Izwak is mostly correct, except I still doubt its the sensors. It could be though. The sensors are Hall effect sensors. The tone ring is metal and has teeth, or high and low places. Electrical current runs through the solid state sensor (essentially a wire and piece of metal) and creates a magnetic field around it. As all wires carrying current do to some degree based on the amount of current. As the tone ring spins its teeth through the magnetic field it alters the magnetic field and therefore the current running through the wire(sensor).
The GEM (located behind the radio, see Brown Wire Mod thread) sends a signal down the wire, through the sensor and back. As this current fluctuates the GEM interprets speed of the TC output shaft. It then compares this to the other sensor for the other output shaft and determins slip and engages 4X4 when the dash switch is set to Auto.
It engages 4X4 via the brown wire. It sends current down the brown wire that energizes an electromagnetic clutch (the ball ramp device in the TC sticky) at a varying duty cycle. Turn the dash switch to 4X4 and it just sends essentially a 100% duty cycle.
Now the bad part. Thats not the only way the GEM determines front and rear axle speed. It also is tied to the ABS computer and a couple others. To determine exactly where the problem is you need to hook a NGS or WDS scanner up and read the PIDs (inputs and outputs).
I had a similar problem 6 months ago, only my auto 4X4 Auto wouldn't engage. After much trouble shooting and failing to secure an NGS scanner I could operate, I went to the Ford dealer. Some dealers don't have them and many that do can't operate them correctly. Luckily Galpin in LA , the largest Ford dealer in the country, does. About $750 later my TC worked. Bad GEM (rare), and one Hall effect sensor reading erratically(not so rare according to the tech). The GEM had an open ABS circuit.
When any sensor fails or doesn't match the other redundent info (ie. ABS) the GEM should default to limp home mode and deactivate the 4X4. This is to prevent mechanical damage. Since yours is stuck in 4X4, my guess is a bad GEM. $319 locally but thats just a guess. Guessing is all that can be done without those scanners.
I would determine the value of fixing the 4X4 before a trade. Our vehicles currently enjoy very little resale value. I would probably just locate the Brown Wire (see BWM thread) under the drivers seat. Its easier to be sure you have the exact one, in my opinion, and disconnect the 4X4 there. You can drive it and not through any codes. You just won't have 4X4 ever, regardless of the switch position on the dash.