First disconnect the batteries....then....
There are two screws on the bottom that take the shell off the base. Once off, you twist the bulb out, remove the two screws that hold the base to the skin. Pull away assembly from skin, may take some finessing since it's been there for 16 years, wires should follow assembly out and tape factory wire side to outer skin (this is so you don't accidentally let the wires slide back in where you have a hard time getting them back), re-cut splice where factory harness meets original fixture, remove old fixture. Clean area well, put a coat of wax on area.
To install, get some shrink tube cut a size longer than the overall exposed wires, and put on factory side- after you strip insulation off the wires on both factory harness/supply lines and the new fixture.
Connect wires together very tightly (or solder it after initial connection), and put a very slight amount of dielecric grease on the exposed wires (not a lot, just a coating). Slide shrink tube over exposed connection, heat shrink tube to tightly cover exposed wires.
Before putting back, reconnect battery and test. Work, go to next step, do workie, troubleshoot.
Where wires immediately go through skin, wrap some electrical tape around it to protect it from contact with the skin, take off tape you placed on factory supply wires earlier and feed wires back into trailer.
Get some silkaflex (or equiv **but not silicone**) place a dab on the holes on the skin (not a ton), push new screws through base and place some silkaflex (or equiv) on the screw head in body. Screw the screws into the same hole, tighten, but don't go crazy tight, the silkaflex will help seal the screw holes and help prevent backout and the foam gasket once tightened will do the rest.
Replace bulb, replace cover done.
That should do it!
PS- Don't forget to mount the license plate bracket the same way it was mounted with the old one...make a note before putting it all back together and replicate that with the new.