If there is a high resistance short between the trailer battery and the camera/running lights, it is unlikely that there is anywhere near 12 volts on the wire. But if the camera has an internal regulator with a lot of overhead, it might still work. Be prepared to measure the voltage at the umbilical or one of the bulbs the next time it happens.
"You cannot reason someone out of a position they have not been reasoned into"
Al, K5TAN and Missy, N4RGO
2002 Classic 30 Slideout
2001 Safari 25 RB Twin (Gone, but not forgotten)
2013 Dodge 2500 Laramie 4x4 Megacab Cummins
WBCCI 1322, TAC FL-39, AIR 82265