A camper has 2 nearly independent electrical systems. A 12 VDC system (battery) powers MOST lights, slide outs, power tongue jacks, the furnace, and control circuits for the water heater and fridge. A 120 VAC (shore power) system powers A/C, microwave, and 120 V receptacles. It also powers a converter which charges the batteries and provides 12 V power in the absence of the battery.
A fully charged battery, NOT connected to a charger / converter should measure 12.6 V.
If a charger / converter is connected and functioning, the battery should measure 13.5 V or more.
Since the battery and converter are connected together, measuring voltage at the power center feed to the fuses should be the same as measuring at the battery, and more convenient. When the lights go off, check the voltage there. If there is power at the power center, then work out from there.