Volkemon,
You are correct with your wiring diagram.
PCs made starting in 2007 until recent years, had that setup with two 12V batteries wired in parallel. In our case, the first set came factory-direct, the second set I replaced with a Walmart brand. I made sure to select a pair with the latest matching production month to help assure they were the same age. Both sets wired correctly had issues where after the second year, one battery became significantly weaker than the other. The imbalance caused the better battery to over-charge (and boil-over) and the weaker battery never reaching a full charge. When I changed to two 6V AGM batteries, the imbalance was completely resolved. They charge and discharge in unison, much like a single battery. With sealed AGM technology, an acid boil-over could never happen, even when the batteries are placed on their side as they are permitted.
It's like every electronic item that uses alkaline and rechargeable "D" "C" "AA" and "AAA" batteries. They are always wired in series (like the two 6V batteries in RVs) for "best utilization" of their available power.
I wonder if two 6V AGM batteries standing upright or on their side, would fit inside your battery compartment.
Sorry serrano4657 for redirecting this welcoming thread. Let's reel it back for you.