The rectifier in the charger is pointed towards the 12V side, so the capacitors discharge due to leakage of the rectifier diodes or other parasitic loads. This is pretty normal and I doubt it has anything to do with the batteries not getting charged from the truck.
You need to check the voltage at the battery terminals with the truck running when the batteries are discharged. When they are fully charged, they will only draw a couple of amps. Spiral AGMs will draw a lot of amps if partially or fully discharged and the terminals are held at 14.5. My guess is that the charge circuit from the truck has a lot of resistance, as many do. When the batteries are discharged, the current goes up, voltage goes way down, and charge rate slows. Most stock truck and camper wiring harnesses have maybe a #10 wire and several light weight connectors between alternator and battery. Many of us have installed a dedicated charge circuit of #6 or even #4 wire, with appropriately rated connectors, to get good charging of the house batteries.
You could try turning everything on in the camper to simulate a low battery, but you then have the camper battery contributing (unless it is disconnected), and that does not check the final few connections to the house battery.