Chris, I'm frankly puzzled. I've never heard of neon tubes used for lighting in trailers. Are you certain they are neon and NOT florescents? A florescent tube will have an opaque glass surface and will emit a white light when lit. And, it will often employ a starter ballast.
Edit: OK, I just looked up T15T8 and they ARE florescents. Follow the steps below.
If that's what you have, and you want to install a complete LED fixture (not just a bulb), you would simply remove that ballast, since it is not needed, and connect the two wires that feed it directly to the two inputs for the LED fixture. You will probably find that one of the wires in the trailer power supply is white, that will be the ground (or negative wire) the other wire is the positive feed. Your LED MAY be "polarized", meaning you will have to connect the positive feed to the positive input side and the ground to the negative side. If the light doesn't light, simply reverse them.
An LED fixture will have the needed components to reduce the 12V DC voltage to the level needed by the LEDs.
Hi-Lo 1707T - Tire Minder TPMS on Tow Vehicle and Trailer, 300W Solar Battery Charger, Equal-i-zer WDH
2014 F150 Platinum 4x4 3.5L EcoBoost SCrew