"RE: "install a jumper wir
"RE: "install a jumper wire between the batteries to connect them together"
This is not generally a good idea. While you have it in your mind that the charger would be supplying current to both batteries more or less equally, the reality of electronics is that current always flows "downhill" and as fast as it can. How this equates to reality in your situation, is that unless both of your batteries are the exact same make and model and of the exact same age and state of charge, then the higher voltage battery of the pair will "charge" the lower one at a rate only limited by the resistance of the jumper wire. If you feel that you MUST do this (keep both batteries on a trickle charge all winter), then buy a battery isolator and charge the two batteries via that device. While charging a battery via an isolator does not result in a 100% charge, the difference in charge level on a "maintaining" charge is minimal.
In like manner, the common practice of boat owners who have battery switches with 1-2-BOTH capability should NEVER have the switch in the BOTH position unless they are in dire straites and this is the only way they can start the engine. Given the heavy cables and low resistance of the battery switch contacts, if there is a difference in the state of charge of the two batteries, a heavy and unregulated current can flow between the two batteries that could warp the plates in the battery.
BTW... one remote but entirely possible scenario of connecting the two batteries together and charging them.... Battery A fails with a shorted cell 2 am one Sunday. Voltage from Battery B flows via the jumper to Battery A. Since there is nothing to limit the current, the jumper wire overheats from the current flow, the insulation melts and the overheated wire starts a fire (since the charger can't regulate the current flow between the good and failed battery). When I was a curious kid, I used to routinely put wires across the terminals of 1.5 volt cells (lantern batteries), just to see them turn red, then white and then burn out. I used bare wires to do this since I learned that the smell of burning insulation attracted my parents attention
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