I know there is a plug dedicated to the steering wheel controls. Why not try this...
Unplug that harness from the factory radio then turn the lights on. If they don't illuminate, then there is your answer. Next you can plug the harness back into the radio and test the wires to see if any of them are supplied with 12volts once the lights are turned on. When you figure out which one does, unplug the harness and test again to make sure that the wire does not register anything. Once confirming that the wire needs 12 volts and is supplied through the radio, you can wire a relay to trigger this wire when the lights are on.
However, I don't see the radio providing illumination. The only connection to the controls is normally data/resistance based. Not to mention that PAC, Peripheral and everyone else making these units would have probably made it known and had an illumination trigger coming out of the SWI-**** box by now. If you can find someone with access to Alldatapro or similiar, you may be able to find your answer.
I still say that installing an aftermarket radio does not effect the illumination.