I recently used an LED lighting product from Lee Valley for a project inside the house -- RibbonFlex Pro™ Warm White LED Tape Lighting System - Lee Valley Tools
While I haven't tried it yet, they look like a good (albeit expensive) solution for various lighting problems in the trailer. The strips use 12V power, and the manufacturer's information says they are suggested for RV use which implies they can handle the somewhat variable voltage ratings we deal with.
The highest density light strips (120 LEDs/meter) provide a lot of light -- probably more than you need (for example) inside a cabinet. But the three different light density strips provide plenty of options.
The stick-on backing make installation easy. The strip format makes it easy to hide the lights and take effectively no room.