I always have a small inexpensive multimeter ($7-$25 LOWES-WALMART-AMAZON ANY NUMBER OF auto parts Stores)

I can place the leads on a battery terminal without SHORE POWER connected and if it reads 12.6-7VDC then I know it is fully charged.
If I plug the trailer into SHORE POWER then the battery terminal should jump up to 13.6VDC or higher depending on what the on-board converter is doing. This tells me the battery and all of the in-line fuses and connections etc are making contact and connected to the on-board converter/charger unit.
If your battery is not connected to the trailer on-board converter/charger unit then it will not be re-charged when plugged into shore power.
Having a inexpensive multimeter around is a very handy tool to have around for us RV'ers.