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Could always install anything from a headlight switch light, to a marker light socket, or an LED to do the same thing. It shouldn't be a very bright light in stock form, the tinyest LED will be in danger of casting too much light.
It's the stubby bit the pink arrow is pointing at, right? That pic is about 20 years old, but that dash shell is still in my attic. I might have to dig into the attic and see if the light is still there.
An alternative would be to install the rear view mirror from a later Firebird. When GM redesigned the dash for the airbag in 1990, they put a provision for a small light in the bottom of the accessory switch panel, but most Firebirds don't actually have a light there. Instead they've got a tiny bulb in the rear view mirror that takes the place of one of the map light switches, and the light shines on the shifter/HVAC/Radio, and ash tray.
It wouldn't be too hard to add the rear view mirror light on an earlier car. Just tap into one of the gray illumination wires in the dash harness, and extend it up the A-pillar with the domelight wiring over to the middle. Then add a ground wire in the center of the roof, that covers two of the four wires, the other two are just spliced into the existing orange and white wires to the dome light. That way the map lights come on with the dome light, or the switch, and the ashtray light comes on with the dash lights.
If you can't fined one, contact firebirddude142, he probably has a few of them somewhere. Now, I'm thinking about buying a couple of extra, I mean geez, if you can't replace the bulb, then that's a problem. Another GM better idea. These cars are full of those.
I'm pretty sure it's neon, or halogen, or one of those... Should be good for the life of the car. Kind of like the one above the headlight switch.
The book shows the Lamp, ashtray with the part number printed on the housing in OP's photo as 87-89. Which makes me wonder, the dash in my pic is from an 86, and as best I can tell it has or had the same light in it. Hmm.
I'm not sure how that light clips into the dash, but maybe something like this LED license plate bolt lights would work? If they're too bright you could always add a colored plastic filter lens to dim them down and change the color. Orange soda bottle might be one way to make it work.