[Carl n Susan]

You might want to check that self resetting circuit breaker that everyone complains about. When they get tired they open. Usually when running a big 12V load (like the hydraulic pump). But that CB goes two ways. If your battery is down to 11.9 (way low!!), the converter is going to want to pour a bunch of amps at 13.6 to recharge it. That heavy a charge also goes through the CB on its way to the the battery. The CB doesn't care which way the 12V is flowing. If it exceeds its (diminished) capacity it opens. When it cools, it closes to allow the 12V to flow again. What is happening is the charger putting out 13.6, then nothing, then 13.6 in a vicious cycle. Dimming of the lights are a symptom of changing voltage.

Stick your head in the front compartment up close to the CB and you should hear it click as it opens and closes.