His problem is not keeping his battery charged, it is keeping the power port hot, to run his Patriot braking system. I would check with eTrailer. I know they make a bypass relay to prevent the brake lights from working with the key off. They may also make one to keep the power ports hot with the key off.
I always hated when we rented cars (foreign and some domestics) where the ports were dead with key off. Sorry to see that Ford is following suit. If my truck was not a 2014, I would be having the same issue as you.
Scotty and Kristen, Airedales Dagny and Wyatt
2007 Newmar Mountain Aire 4528, 450 HP ISM, Allison 4000, 8 Trojan T-105's
2014 F150 4x4 Crew Cab Platinum 157" WB
Roadmaster Blackhawk 2, RVI2 Brake System