All trailer wiring I have encountered is pretty basic, not a lot of wires. Which makes it pretty easy to trouble shoot if one has a basic understanding electrical wiring. 12 volt DC or 120 AC.
There are plenty of websites that give a great education information. I am sure there are people who have put up sites explaining how to trouble shoot trailer wiring.
12 volt DC lights are very safe to work with. Most but not all trailer and or truck/car side plugs use a universal wiring pattern. There generally is no dedicated “wire” for interior lights. The “hot” wire, power supply wire for the lights, usually red, is “tapped” spliced to the a “powered” wire coming from the vehicle. It depends on how the manufacture went about things.
The trailer manufacture’s website might give the trailers wiring diagram. Which makes things easier to troubleshoot.
With lights there are only a couple of things that can go wrong. The bulb is blown which is easy to figure out, the switch is bad, that doesn’t usually happen, 1 of the two (or 3 if there is a green ground wire) wires, positive (usually black or red) negative (usually white ) is broken, disconnected somewhere.Or there is a bad, disconnected ground. Some lights have a ground wire (green) some light fixtures are “grounded” to the trailer by the attachment screws or rivets.
Interior lights usually draw their power from the power supply line for the running lights.Some, a lot of trailer running lights are come on when the vehicle is running. Some only when the vehicle’s lights are on. Depends on the manufacture’s wire harness or how it was installed, wired “after market”.
Buying a basic wire test light make/helps figuring things out a lot easier. They can be had for $5-10+ something like this;
http://www.homedepot.com/p/GearWrench-Low-Voltage-Circuit-Tester-2646D/205594354?cm_mmc=SEM|THD|G|0|G-Pro-Services&gclid=Cj0KEQjwzpfHBRC1iIaL78Ol-eIBEiQAdZPVKjmhnGC9FPkDrRphM8gckvJ3KRKFcKt-MsL_Ga3dYTwaAhpF8P8HAQ&gclsrc=aw.ds
The wire that has the clip on it is the ground, clip it to green ground wire or to non painted metal. Touch the “pointy” end the power wire, red or black. The light in the tester will come on if there is power going to the light housing. If not you have to determine if the problem is with the power supply wire or the ground.
Shouldn’t be hard to trace/follow the wiring back to the where it connects with the all the wires going to the vehicle. Take the tester clip the grounding wire to clean metal or a green ground wire. The pointy end is sharp enough that it can be pushed, pricked through the plastic jacket of the power wire with out having to strip the over coating off. If the test light comes on. There is a bad part of the wire from this point back to the light fixture.
If there is power at the light fixture either the bulbs are blown.or the bulb housing bulb contacts have fatigued and not making contract with the the bottom of the bulb. This can be bent back into shape to make contact.
The above is assuming all of the relevant fuses have been checked. .
The problem may be on the vehicle wiring harness side of things. But if the running lights work, break and turn signal lights work, electric breaks work everything should be in order. But you can use the tester to check. The truck side power, Touching the ground test wire to the round pin and the pointer on the desired “power pin”.
If the vehicle “plug” has a flip up/down cover the wire coding is usually stamped on it. You have to look carefully. The wring diagram that Brian linked to us pretty universal .
This is a very good page that gives a lot of details for various types of trailer wiring.
https://www.etrailer.com/faq-wiring.aspx