Jim,
As you know the marker lights are powered by the tow vehicle. The electric
jack, water pump, and interior lights/porch light, etc. are power by the
trailer battery.
The only thing these two items have in common is the ground. I would check
the ground wire on the battery in the trailer. Follow it from the negative
terminal to where it connects to the trailer chassis or other ground wires
that it connects to. Your just checking for good solid mechanical
connections and no corrosion.
Also, check the ground on the cable that connects to the tow vehicle. Make
sure that has a good ground from the tow vehicle to the trailer.
-Tim