It seems as if your rear battery isn't even connected to the electrical system, though this is implausible.
I think you are simply going to have to check power distribution throughout the vehicle with a voltmeter. I've attached a diagram of the electrical system to provide an overview. Likely you'll need more detail to make voltage measurements, and for that you can download all of your vehicle's wiring diagrams here: R230 ETM 64. Double-click on the msi file to install the diagrams along with the parts locator program Starfinder.
I think you are simply going to have to check power distribution throughout the vehicle with a voltmeter. I've attached a diagram of the electrical system to provide an overview. Likely you'll need more detail to make voltage measurements, and for that you can download all of your vehicle's wiring diagrams here: R230 ETM 64. Double-click on the msi file to install the diagrams along with the parts locator program Starfinder.