There is an instrument panel illumination feed going to the factory unit, it is powered by the same power feed that backlights teh instrument panel.
In your case, Id say the backlight switching transistor has failed or the backlight itself has failed. Those old radios are 20 years old, many of us have tossed them, I tossed mine in 2015 for a JVC.

Just get over it and put a REAL radio in there, one that supports four channels. Then look in this sub forum for the thread on how to modify your amps' wiring to four channels and you willl have fader as well as balance control.