Looking at a trailer with a 12 volt fridge and solar panel mounted on the roof. not sure of the size of panel. My question is this. how can i tell if the panel is charging the battery?
You should be able to put a multimeter on the battery during the day and watch the voltage or look at your charge controller to see if its charging the battery.
As far as keeping the battery topped off while in storage - if you have a battery disconnect switch which will stop all power from going into the trailer and your charge controller is hooked up to the battery it should keep it charged and topped off - thats how my setup is