What to use to keep battery charged while sitting?

I have a 10w solar panel that keeps the batteries charged with the battery switch on, and even charges a little with it off.

I would install a good battery disconnect and a small 10-20w solar panel. In 2-3 weeks there should be minimal drain with the batteries disconnected. Then if you want to precook the fridge the 10-20w should be plenty for 24-48 hours.

I would also have your fridge checked out.