Hello Andersojd (1972 Argosy 22),
The wiring will not be your problem.
120v typically has 3 wires Black (120v hot), white (neutral), and green (ground).
On your trailer Black should be (12v hot), white should be (ground).
Meter yours to make sure.
On a 120v fixture conversion, the black will become the (12v hot), the white will become the (ground), the green will become a spare as it is not needed on a 12v
That being said, your issue is, now you have to get 12v
lights for the fixture, or change the sockets to accommodate a 12v
light or LED. Doable, but not so easy. It may require rewiring the entire fixture.
In my opinion it would be easier to search for actual 12v light fixture options on line. Like a marine supply store or something like rvupgrades.com, etc, etc.
Maybe not so easy to convince the wife, lol.
I hope this helps. Best of luck.