Could be as simple as one filament of the bulb being burned out. There are so many different types, it's hard to say how to remove the bulb from your particular lights; just examine it closely and I'm sure you'll find out. Some lights you have to remove the lens (a few screws around the perimeter) and others have a fitting on the back that you remove.
If it's not the bulb, and assuming the trailer has standard wiring, check the connection from that light to the brown wire; brown feeds the "running" lights, side marker lights and tag light.
And welcome to the exasperating world of trailer lights!