Battery help.. question for the battery experts

I would install them both. Wire them like Piano says.
Someday you may need to dry camp, or some day the power may go out, either at home or at camp. That extra battery would come in handy then.
As for your Trickle charger, yes, it can be left on 24/7/365. If you wire them as suggested even while charging, they will be pretty much on auto pilot. Check the water once a month or so, and call it good.