I just bought my third deep cycle marine battery in three years for my Rockwood Fifth Wheel. They keep going dead. I bring them indoors in winter and keep them connnected (plugged in) in the RV all ...
And you aren’t wanting to check an inverter. The proper name is converter and each performs differ t functions. Measure the DC voltage as stated and skip all this other stuff. If you don’t see 13 plus volts when hooked up then you have a converter issue and the batteries are not charging.