Pick a sunny day. Disconnect the trailer from shore power and and cover the solar panel with something opaque (cardboard, etc.). Check the battery voltage with a multimeter. Uncover the solar panel and check the voltage. You should see a slight rise.
If you don't see any difference, run a few things on the battery for a bit to discharge it some. You can do this by lowering and raising it a few times, running the refrigerator on battery power (not propane) for an hour or so, etc. Then measure both voltages again.
If you see a voltage rise in either case the panel should be working. You may want to use a digital multimeter because the difference may not be enough for an analog one to pick up.