Just happened to us-- 2015 F150, 2013 25 RB FC. Last day of a wonderful 10 day SW Oregon Caravan. Had just had the plug replaced a month earlier; new one had wires attached with crimper that left a bad attachment in the plug.
The F150'a 'disconnect' signal was not 'false.' Problem was with the bad connection on the wire that controlled trailer brakes (and thus also the brake assist)(all the lights and turn signals worked fine). If we had ignored the 'disconnect' signal, we would have been trailering w/o trailer brakes, potential disaster just around the corner!!
Best part of the story-- a group of fellow AS'ers worked with me in the rain (holding umbrella, guiding small screws on plug, general advice, and more) to reattach cord to plug with good crimp work.
Drove safely home on OR 101 in driving rainstorm, thanks to brakes that worked because of these good Caravan'ers. Thank you Jim, Dan, Bill and Dan.