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Is the O/D light or the 4x4 light flashing by chance? That will let you know there is a fault in the module. If not, then the issue may be mechanical or 2 separate issues going on.
To test the transmission modules, you will need the Ford IDS scan tool on and monitoring the transmission or a simialr scanner with the capability. This way when it is shifting, the tech is recording what it going on and monitoring the shift points. They can also see the voltages on the solenoids to indicate if the issue is internal of the transmisson with the solenoids, a mechanical issue, or if the issue is in the transmission controller.
With an issue as unique as this, I would have a transmission shop look at it. AAMCO does a lot of the checks for free or for a low rate. I would start there for they can test it right quick and it is cheaper than Ford. Another option is to have the vehicle scanned at Autozone for transmission codes. They can do it for free. It will narrow down if the issue is electrical and where to start.
I suggest this because that module that is being referenced, the ESOF aka 4x4 module is about $400 plus the cost of programming. The transmission shifting is done by the PCM and that can range from $300 to $600 plus programming. I'd hate to blame a module for an issue like a short to a relay in the GEM module aka fuse box or a solenoid in the transmission that costs around $30 and just shy of $85 for the labor. I rather have it tested for codes and a shift pattern issue first and go from there.
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