Converter Issue?

Or just don’t worry about it unless you’re trying to band-aid a “dumb” converter that doesn’t know when enough is enough.
You could put a disconnect just downstream of the batteries or re-connect the converter on the downstream side of the existing disconnect.

I guess both of those options are fine if you don’t want to replace your existing converter with one that it won’t matter whether you leave the batteries hooked up. (If that’s even an issue, you didn’t say, but it’s the most plausible reason for your question. Imo.)

If you have a modern converter, add a switch at the battery bank. Use that to isolate them for storage. Leave the oem switch set to use.

You also stated you checked the INVERTER. Was that a mistake, you meant Converter, or do you also have a Inverter? Doug

Yes, EVERYBODY(not experianced in the RV operations) seems to think they KNOW how things are supposed to operate. Just because THEY own an RV:)
Problem is, RV's are NOT cookie cutter products. ALL have different parameters and how they are set up. So, to answer your question which you have found out the answer already. YOUR particular OEM decided to connect the Power Converter on the HOT side of the disconnect solenoid. Some connect on the Cold side and some connect on the HOT side. This means, your unit is connected on the hOT side. Hot is the side that goes TO the coach batteries. So, when you turn the disconnect OFF, you found out that when 120 shore power is ON, the Power Converter is NOT supplying 12 volt power to the RV. There are multiple reasons for why OEM's have different ways to connect the Power Converter this way. The simplest in older RV's is you really want a LOAD(coach batteries) connected to the Power Converter when shore power is connected. This helps regulate the charge function of the Converter to the batteries. Having the Converter on the COLD side, when disconnect is OFF, means you DO get 12 volt power to the RV and the Coach batteries are disconnected, which means they will go dead after weeks from parasitic draws on the system. This used to be common place 20/30 years ago when fulltimers or people that used their RV's weeks at a time. Someone accidently pushedthe 12 volt disconnect and since the 12 volt systems in the RV functioned they thought everything was OK. But, they then disconnected shore power and had NO 12 volt. They realized that the disconnect was OFF, but when they attempted to turn the disconnect ON, they found the Coach batteries dead. So, the disconnect would not function. You CAN move the Converter 12 volt power lead to the cold side of the solenoid to accomplish 12 volt power with the disconnect OFF. Some older Power Converters NEEDED the batteries connected to get the beat 12 volt regulation and charge. Doug