Nell:
I believe the converter is rated to deliver up to 50 amps of 12 volt power. Most lamps use 1 to 5 amps. If your battery is not going down, I would assume that your converter is working to some extent. My first guess would be a poor wiring connection somewhere in the 12 volt distribution. Using a digital voltmeter take a reading across the battery with the trailer unplugged, then the trailer plugged. The 2nd reading should be higher, indicating that the convertor is working. Next take a reading across the battery with all the 12 volt lights and devices you can think of on. The reading SHOULD be about the same as the reading with little loading. If not, you may have a converter/wiring/connections from the converter to battery problem. If there is no change between loaded and unloaded 12 volts at the battery, you next need to repeat the loaded/unloaded readings test at the fuse panel. If there is a difference there, then you have a wiring/connection problem between the battery and the fuse panel.
BTW, do your 12 volt fans slow down when the lights dim? If not, you likely have a problem in just the lighting wiring.
When you are doing the full load test, you can move wires at connections looking for light intensity changes. This indicates a poor connection. You can also feel the 12 volt connections for heat. Heat is a sign of a poor connection. 12 volts DC is not a shock danger to touch with a bare hand (watch out for jewelry shorts, though - Jeep enthusiasts WELD with 12 volt batteries in the boonies!). DON'T TOUCH ANYTHING YOU EVEN GUESS IS CONNECTED TO 120 VOLTS AC!
These poor connections are like kinks in a water hose, that change the amount of water flow (like electrical current).
Good luck!
