Since LED are polarity sensitve, we have a bit more trouble sorting out which is battery and which is ground as the fixtrue often looks the same. But the idea is still the same in that there has to be a path for power to get to the LED and also one for it to get back to ground.
Full circle is a good "circuit", so I look at the two connections and expect to see one power and one ground. If I'm missing one or the other, I know whether to chase the power or ground side and that cuts the chase in half!
I've not looked at trailers in a long time and we don't get the best info on them, so I wonder if the wiring has ID stamped on them like motorized?
That might give you a head start on which goes where and does what?