Will you be towing this primarily with a civilian or a MV?
If civilian pickup, you can rewire the trailer from the 12 pin plug to a 4 pin (or 7 or what have you) and plug it directly into your vehicle. Replace the bulbs with 12v lights and be on your way. The 24v lights work, but are dim.
To pull the 12 pin connector apart, remove the clamp at the back of the connector, apply pressure on the cable into the connector, lift and lock the cover open, then carefully pry the rubber & pins out with a small screwdriver. Unsolder the pins necessary (I would have to search for the wiring diagram again, but I know it's here) and put them onto your new connector.
If going to be pulled by a MV and civilian, wire up a secondary connector pigtail from the vehicle to the junction box with the appropriate civilian plug and some crimp bullet connectors, then replace the whole cable end, takes about 5-10 minutes with a screwdriver to make the switch and no other lights are necessary (again, you'll be using 24v bulbs). Just match up the wires in the junction box to the wiring diagram and you'll be all set.
HTH