I can see wires under the trailer leading to each end of the wheels. Is there any way to see if the brakes are functional?

Jack up the trailer, spin the wheel, then apply 12v to the brake circuit. See if the wheel stops, etc. If is does not, it may be an electrical or mechanical problem. Could be bad wires/connections in the frame harness.

They are just a simple magnetic coil that pulls an arm to engage the brake shoes. Check the wires for continuity through the coil. If coil sems OK it is likely just rusty parts.

Gold standard: Pull the hub and inspect shoes, levers and coil. Clean and lube, regrease the hub bearings, drive for long time…