A 13 ft. trailer this age shouldn't be hard to "rewire", if needed.
Since there's no converter, 110v and 12v should be independent of each other. Do make sure of this point- no hole where a converter might have been removed, no 110v wire that ends nowhere....
110v (shorepower) likely enters the trailer to a 15 amp breaker, and is distributed to an outlet or two and maybe a light. That will be ordinary house wire. IF this is 3-wire, you can probably keep it. If it's only 2-wire, it should be replaced.
12v power comes in from the TV or battery via the pigtail, and is automotive multistrand, color coded.
My first advice would be not
to tear anything out until you're sure it has to go. If it's original wires, they're an excellent "map".
Is the wiring for your lights, etc. inside the trailer? I hope so...
Unless somebody's been at it before you, or mice have chewed it to pieces, the inside 12v wiring is very likely fine, and still in the original colors!
That would be good news for you.
The same could well be true of the 110v.
Have you tried anything, such as the taillights, etc? Did you tow it home?
And does it have brakes? A 3-way fridge?
What does the trailer-to-car plug look like? (4-flat, 7-round, etc.)
Here's a 12v wire chart that should apply to a trailer of the same vintage:
(doesn't matter if you have the plug this chart talks about, or if you lack brakes or "auxiliary" wire. What you DO have should be in the colors named for the particular fixture.)