You can easily check if you have voltage to the lights before you change them out. With a multi meter, put the + lead on the wire going to the bulb's base, and the black wire on the trailer's body where the bare metal can be touched. If you have 12v the bulb's socket is probably bad. If not, the wiring to the light base is bad.

Ospho is an excellent rust converter. Once the old caulking and loose rust is removed from the roof, the Ospho will stop the present rust and act as a primer for any other application. Marine caulkings are much better than the household types found at the big box stores.

The "clear stuff" can be removed with a sander. Another product called an elastomeric coating, can seal and weather proof the whole roof with an easy roller/brush application. It will result in a white roof that is heat reflective, and will stop any further rusting. Depending upon the size of your roof, a five gallon bucket can result in two coats, at a cost of ~$90. The better products are warranted for 10 years and can be easily recoated.