Both my A-frames had automotive stereos installed, and both had the issue you had. I traced it down to ANY sudden DC voltage change turned the stereo on. It could be turning the disconnect switch on/off, plugging/unplugging the camper (turns the converter on/off), etc. So I decided to install a separate power switch in the positive 12V lead of the stereo. When I pulled out the microwave to access the stereo wiring I understood what was happening.
An automotive stereo has 2 power leads. In a car or truck, the main power runs through the ignition relay, so that relay has to be on for the stereo to power up. The second power lead bypasses the ignition switch to provide "keep alive" power for presets and memory. If you remember replacing the battery in your car or truck, you remember losing all your radio presets and equalizer settings - because both wires are unpowered when the battery is removed.
Since campers don't have an ignition relay, both the keep alive and main power wires are connected to the same unswitched +12V DC source. A quick voltage change has the same effect as the ignition relay being turned on in your car or truck.
My cure was to install a switch in both stereo power leads. I didn't want the current draw of the stereo "keep alive", even though it's quite small. Losing the presets and other settings reverting to default was worth the power savings, since I rarely use the stereo while camping. But if you want the "keep alive" function, only switch the main power lead.
2019 Flagstaff T21TBHW A-frame
2008 Hyundai Entourage minivan
camping Colorado and adjacent states one weekend at a time