I did this years ago in my '95 Lumina... all the bulbs went out in the radio, plus in the Thermostat/Climate area.
Dealers solution...replace radio, replace Climate control unit, no user serviceable parts.... Poor answer & even yet poor design, to this day GM DOES NOT use LED'* in these 'non servicable' applications.
I never got to the climate control due to aging issues in the dash plastic, however I did replace 2 of the 3 in the radio... soo after the 3rd bulb went... should had done em all when I had this apart..... but IMO these bulbs should last for decades, & they sometimes do.
I'm not sure but I believe I just used lower wattage 12v grain of wheat bulbs I had picked up at Radio Shack, or I modified a #37 bulb ... these had to be hand soldered, plus you can't use too high wattage as these are close to the lexan/plastic overlay, & may deform, this. I tested for a few hours before re installing, no heat problems.
The bulbs in my Camaro'* radio are now getting fickle, a little rap on the dash sometimes helps too!
(but this is temporary)... no wonder people go over to aftermarkek radios, at one time Delco made a bulletproof radio, now it seems inferior at 4 to 5x the price of aftermarket.