Some great advise here.
Was thinking. Since you don't have power at the building, solar would make a great trickle charge.
However, your issue of drain probably exceeds the charge your solar will provide on those overcast days.
Have you considered installing a cutoff like this? You could mount it under the chassis somewhere easy to get at. You would still be able to trickle with solar and completely isolate the batteries.
Steph and Eden
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