Hi Jim, welcome to the site. Congrats on getting a new to you trailer.
It could certainly be a few different things causing your light
Do the tail lights
and marker lights both come on fine. If not I would start with the bulbs to see that they are good. Also check the ground to the fixtures.
If the tail lights
work, it is more likely something amiss with the wiring, something you would need to wring out right from the vehicle connection. Using a meter you could check continuity from the plug to the light
itself, and if there is nothing you then need to trace your way back.
I am sure others might have some more insight too.
Failing that, a trip to a shop that can check it out might be in order.