Interior wiring on trailers is very simple. Rarely does it get complicated. As you can see from this schematic, every fixture requires 2 wires to make it work. For 12 volt appliances, you need positive and negative. For 120 volt you need a positive and common or negative. Most old trailers didn't use a ground wire so there won't be any connections for a ground.
NOTE: THE WIRING YOU USE SHOULD BE RATED FOR THE SOURCE. USING UN MATCHED WIRING CAN RESULT IN FIRE FROM OVER HEATING. PLEASE CONSULT A PROFESSIONAL.

Most vintage trailers didn't come with any 12 volt lights, and it's very nice having them, so I'll discuss adding lights and this should help anyone needing to fix a light.
In this trailer, I am putting in a new ceiling and so I can run my wires on the outside of the existing ceiling.
The ceiling will have 4 lights with one switch.
So here I have brought A 12 volt source which is marked with masking tape.
I have all four wires for each light coming to this point.
And I have a wire running to my switch by the door, also marked.
First I connect all the negative wires from each light to the 12 volt negative source. I'm half done.
Next I connect the 12 volt positive source wire to 1 wire going to the switch. (doesn't matter which wire)
Next I connect the positive wires from the four lights to the other wire from the switch. When the switch is turned on, electricity is sent to all four lights.
Done

The biggest trick in adding 12 volt lights is figuring out how to hide the wires. There's no easy answer to this. You just have to get creative.
Here I've cut a hole in the existing roof so I can stuff the excess wire into it after I install the light.

Then I ran the wire down the frame of the cabinet, stapling it as I went. This is where the switch will be placed.

To install the light, strip the wires, twist them together, wrap them in black tape, screw in the light and you're done.

The light switch was just a wall switch. Cut a 1-1/4" x 2-1/4" hole with your jig saw and screw the switch to the plywood. No need to use an electrical box as 12 volts can't hurt you. (where's that damned screw)

This is a typical 120 volt connection found on the outside of a trailer where you will connect the trailer to a 120 volt source. You can simply plug in an extension cord to supply the trailer with electricity.

This is a typical 120 volt fuse found in vintage trailers. It's an old style glass fuse. They work fine and the fuses are still available. The electricity comes from the outside plug to this fuse. It is then distributed to the appliances. If there is a short circuit, the fuse will blow to avoid starting a fire.

This is the back side of a outlet. The outlet is housed inside a box to protect it and to keep occupants from getting shocked. On this outlet, the connections are outside the box because it's been modified. The owner ran 2 new wires to another fixture. There is nothing wrong with this type of modification as long as the connections are covered. Note the plastic wire nut covers that are used to insulate and connect the wires.

This is a typical 120 volt light. From the fuse the wires will run directly to the fixture which has a builtin switch. To connect the fixture, you'll have 2 120 volt wires and 2 wires from the fixture. Connect 1 wire from the fixture to 1 wire from your 120 volt source by twisting them together and twisting on a wire nut. Do the same with the other wire. It doesn't matter which wire is connected to which. Then stuff your wiring into the hole and attach your fixture. PLEASE FOLLOW ALL MANUFACTURES GUIDELINES.