My POPUP trailer Jensen radio would turn OFF at the radio ON-OFF button but everything would go off, channel setting, clock etc...
I found the hot wires were tied to together behind the radio. This JENSEN was a auto radio so it has one main 12VDC connection with the fuse inline and then it wanted to have a second 12VDC line coming from the ignition key on-off swithc. I separated the two wires and ran the ignition wire to a Radio Switch.
Now when we arrive at the camp ground area I can turn on the main radio and make all of of my channel button setting and reset the clock etc. Then when I turn off the radio I use the radio shack switch only.
The main 12vDC keeps all of my presets.. this is sort of opposite what you was wanting haha... You can see the radio shack push switch beside the radio install labeled RADIO... This is my ignition key haha...
Roy Ken