I repainted my 17 foot Boler
this spring and in the process removed the marker lights. What I found was the marker lights had positive leads connected in series to each other (each bulb fed the adjacent bulb). These positive leads are black. To complete the circuit, a white ground wire goes around the inside perimeter of the trailer behind the insulation. A lateral lead is taken off this main ground to each light
to complete the circuit. You may not notice the ground as it is connected behind the base of the light. When you remove the lense and see two wires, they are both positive. At least this is the way mine was wired.
If you connect the lights without the ground they will still work but your voltage is cut in half with each light connected. In other words if you have one light connected, you will have 12 volts, two lights connected, you will have six volts and so on. By the time you have all 11 hooked up they would be so dim you probably wouldn't notice them on. Connecting the ground eliminates this problem.
The white wire you found is probably part of the ground circuit for your marker lights. If you check for continuity between the white wire and the frame and it is a ground, you could run a jumper wire from the white one to the frame and try your marker lights.
Good luck. Also, the old marker lights in these trailers are notorious for bad connections just by the nature of their construction. I replaced mine with a very similar marker light with a plug in type bulb from Princess Auto that were about $3 each.