When you turned thermostat OFF and back on this cleared the “lock out” condition the furnace experienced. After 3 unsuccessful light attempts the furnace control module goes into lock out and can only be cleared by turning thermostat off or killing ALL 12vdc to RV..
The water heater has its own control module and is a separate issue.. if 12vdc to both modules gets much below 11.5 volts neither will operate
Are you certain converter and battery are providing over 13 volts DC if plugged into shore power?
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