Hate to say it but there's not going to be any manual for that trailer.
Know that there are two 12 volt systems on the trailer. The taillights/marker lights are one 12v. And the interior (water pump, lights, furnace, vent fans etc) are the second 12 volt system. The interior lights water pump, fans and such are still 12 volt even when plugged in to shore power.
Are both 12v systems bad or just the taillights/marker lights.
If only the taillights/marker lights are you testing with the trailer plugged into the tow vehicle? Or are you using the onboard battery and some test leads?
I'll say you're probably on the right path looking for ground problems. Try looking on the tongue. Follow the negative battery cable from the battery post to the frame. Pull that attachment bolt and clean up the ground point so it has bright shiny metal.
Follow the positive cable from the battery to the trailer. Somewhere along the line you'll probably find a 12v circuit breaker. is it in good shape or all rusty? If rusty pull it off and take it to the auto parts store and get a new one with the same rating. If the rating label is all worn off I would probably start with a 25 amp one.
If you are testing when plugged in to the tow vehicle; Get a set of jump starting battery cables. Make a good ground connection from a bare spot on teh trailer to a bare spot on the tow vehicle.
