Unless you are certain you have a multi-stage charger, I'd go with a battery tender and leave use/store switch in 'store'.
The battery tender can handle the parasitic loads. Do check your battery water level at regular intervals.
Best way with two parallel
12 volt batteries is to connect to one terminal of each battery to even out the (very minor) losses in the interconnecting cables.
This is what I would do in covered storage. My rig has enough solar and a good controller, so I leave the DC stuff on so my fans will run if the AS gets too hot. I do check the water in the batteries regularly... (thanks for reminding me)
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Rich, KE4GNK/AE, Overkill Engineering Dept.
'The Silver HamShack' ('07 International 22FB CCD 75th Anniversary)
Multiple Yaesu Ham Radios inside and many antennae sprouting from roof, ProPride hitch, Prodigy P2 controller.
2012 shortbed CrewMax 4x4 Toyota Tacoma TV with more antennae on it.