If it is a Bose system,...Get a flashlight. On my '90 the radio light bulb is non-servicable and to fix it you will have to send the unit in for service.....SURPRISE! Yes, it really sucks, just for a 50 cent bulb. Corvette Central has a service listed in their C4 Catalog page 142. All for the (It's a Corvette so screw me)price of $229. plus shipping. Personally, I just remember what I have on which presets and as far as the clock, I wear a watch and usually have my phone handy too. Sorry to be the "dark cloud" of reason, but getting the radio out requires dis-assembly of the console and the center section of the dash. Plus it is probably a few week turn-around. So by the time you get your radio back you'll have forgotten which screw goes where, because they are different...Naturally... Not a picnic!
Hint: I keep a mini-maglite in the console(with batteries). Something you should do anyway, just in case, for a multitude of reasons. Do you really trust your under-hood or spare tire lights?