[atreis]

If it wasn't being charged, the battery getting low after two nights is about right. (It's also running the control circuit for the fridge, various safety devices, water pump, possibly more, and you were likely not making any attempt to conserve.)

If your converter is working, and your battery is low enough for the lights to be dim, simply plugging in to shore power is enough to see. (The lights would get bright.) You can also measure the voltage at a 12V receptacle, or at the battery itself before and after plugging in. Before replacing the converter though, check the circuit breaker. Usually the converter has it's own. If it looks like it's on, flip it off and back on. (Sometimes a tripped breaker doesn't look tripped.) FWIW, it's not that unusual for converters to fail.

The suggestion about contact cleaner makes me think the electrician isn't familiar with how trailers are wired. Your connection to the battery is clearly fine, and assuming you used 110V appliances (AC, microwave) the connection to the converter itself is also fine.