How old is your battery?
If your battery is very weak it could lose it charge over time even with it disconnected from the trailer. When you first connect the battery the voltage is most likely too low to light the lights.
Connecting the Converter will allow it to TRY and charge that low (almost totally dead) battery. That will make a buzzing sound as it tries to bring the voltage up at its highest charge stage. If the battery were any lower it may not have worked at all. There is a safety circuit in the converter to prevent it from damaging itself from a shorted or dead battery.
After a few minutes, that battery will be charged enough to supply 10 or so volts and the current to light the lights bright enough for you to see.
IMO, you most likely need a new battery and some kind of battery maintainer to keep it healthy.
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW