If you are able to use your ceiling lights without the shore power cable plugged in then you will have a battery on your trailer...
Good way to tell is use a multimeter across the battery terminals and it should read 12.6-7VDC if fully charged. Then plug-in to shore power and you should see the battery DC voltage jump up to 13.6VDC telling your the converter/charger is working...
You will have to provide the converter/charger model number to tell us if it is a single mode or smart mode type charger.
Most larger trailers trailers have a 45 or 55AMP size converter/charge unit. My POPUP tent trailer came with a 30AMP converter/charger which I changed to a PD9260C unit to charge my bigger added battery bank...
You probably have the C17 TRAIL LITE trailer...
TRAIL LITE TRAILERSRoy Ken
