Good luck on the LL... If you are past warranty... It is yours, most likely.
Honestly... For Ford issues, might be best to ask on a Ford forum...
If it is "yours" and repairs are in you, read on...for a few questions...
First question... Are you a capable mechanic and assume all responsibility..read on..
... Since this appears to happen around time you tow, it seems to me it might be caused by chassis torque.
... Have you checked then "grounds" between motor and frame and negative side of battery?
.... What happens if you at unhitched from AS, then "power brake" a few times?
The pony being trying to find a bad electrical connection which could Cause this problem... It might be in the wiring bundle where it enters the cab...
Peace and Blessings..