Do these lights [b]"ONLY" run off of the 12v battery?
This will depend on how the converter is installed and wired up. There are 2 different ways it is wired.
I have observed that some
trailers consider the converter to function more as a battery charger than a power transformer. Thus, the 12 volt battery must be in the circuit
for the 12 volt appliances (lights, water pump, heater blower motor) to function. No 12 volt battery, no functionality of these appliances.
trailers (like my 16' Fiber Stream
) more commonly connect the converter to perform both functions; battery charger AND power transformer. I can disconnect my battery and my converter will run the 12 volt appliances from the 110 volt source, transforming it to 12 volts DC for those appliances.
Both ways of connecting the converter are equally common, yet many owners assume the latter.