Keep it plugged in to keep the new battery charged fully.
I used to do this but now I am not so sure this is a good way to go after dealing with batteries in an electric golf cart.
I know my camper converter continuously will output approx 13.7 volts. After my last outing on battery power only, I came home and plugged the camper in where it has remained plugged in to shore powere for the past 5 days. The camper converter is still outputting 13.7 volts after 5 days. The thing I don't know is what amperage the converter puts out.
By now the batteries should be fully charged and the way to confirm this is to let the batteries rest for 24 hours and check the voltage. 12.73 volts would indicate a fully charged battery after resting, assuming good batteries.
I worry that leaving the battery charging for extended periods of time could deplete the battery acid solution due to off gassing, leaving a dry cell and a ruined battery.
I know my electric golf cart battery charger shuts down when the batteries are fully charged and an automotive automatic charger will do the same.
