Yes! It would be really beneficial to see the wiring from the plug to the radio chassis including the radio switch. I can't figure out what the "logic" should be.
I assume the TV should have priority so if the radio is turned on, it will be turned off if the TV is turned on. Beyond that, tis a puzzle... When the TV is on, should the radio perhaps be in "standby" mode with heaters warm, or should it be *dead cold off*. If the radio switch is on, should the radio lights be left on when the TV is on, to perhaps indicate that the radio is in standby? Should the TV be in "standby" or "dead cold off" when the radio is on?
good puzzle,
jr