I dont have the schematic, but I do have a pin out. It shows pins 13/14
as the 14V Power input. Pin 1 is the Power Ground. Pin 10 is the
Dimmer input.

The internal lamps will light up when ever the dimmer bus is alive,
whether the radio switch is on or off. Are you sure that the radio is
really powered with the switch off?

If so, the internal power switch may have failed. There is no wiring
at the rear connector which would cause it to be on permanently.