years ago i bought an exchange radio at a jag dealer, i plugged it in at the dealer parking lot and it worked, so i came home , only to find out that the radio does not shut off when ignition is off ,! for various reasons i have not been concerned, but now i'd like to fix it.
does the switching occur inside the radio ??
thanks for any help.

 

Using a bit of outside thoughts here, and what I found on mine when I replaced the head unit, so take what you want.

The radio/wiring is no different to any other radio that I have found.

It has one wire that is 12v HOT, which is for the memory function, Another 12v wire is acc/ign switched. Colours now elude me, but simply pulling the unit out, and a voltmeter will determine which is the HOT wire (usually solid Brown on Jags), and which is the 12v switched (maybe Brown/black trace). If the plug from the car loom is doing what it should, as in the 12v switched wire going "OFF" when the ign is OFF, then the issue is inside the radio, which is my guess anyway.

 

Sounds like something is wrong with the radio, i agree with what grant says. I swapped my radio for an aftermarket and got a wire harness to install an aftermarket from ebay with the fascia as well for 75$, worth every penny and makes installing a new single din radio a breeze!