There is a connection to the trailer battery in the TV umbilical, along with the all the clearance, tail, turn and stop lights. This connection may, or may not depending on the phase of the moon when the trailer was assembled, be broken by the STORE/USE switch. I'd look for corrosion or moisture in the plug on the cable, crush damage to the cable, and a final option (because it may be hard to find/get to) is to uncover and inspect the black plastic box that terminates the umbilical inside the trailer. Perhaps a loose connection has allowed a terminal lug to slip.
"You cannot reason someone out of a position they have not been reasoned into"
Al, K5TAN and Missy, N4RGO WBCCI 1322
2002 Classic 30 Slideout -S/OS #004
2013 Dodge 2500 Laramie 4x4 Megacab Cummins