Is my battery being properly charged when TT is plugged in?

I leave mine plugged in all the time to keep the battery charged up by the built in Inverter/Charger. When in storage I pull the battery out so that it does not run down due to phantom power sources and the propane detector.
I need to install a battery disconnect switch so I don't have to keep removing the battery when put in storage since I don't have access to hydro at my storage facility.