In my rig, with the switch set in "Chassis", when the engine is turned Off, the radio (if On) goes Off; it will come back On when the key is turned to On.
When set to "House", the radio (if On) will remain On, regardless of key position.
The radio should be a Winnie responsibility, as well as the "Chassis/House" switch; but the key may be Workhorse.
03 Adventurer 38G, W22, 22.5 Whls
Koni FSD's, TracBar rear, SteerSafe, 50A SurgeGuard, Eternabond; 2012 Honda CRV EXL w/Nav & AWD