See can you disassemble the switch for anything corroded/broke/worn.
If not takeapartable then some spray elec contact cleaner
If nonathat then glop the switch full of dielectric grease and cycle 100x
Or, try to order a new switch
You didn't list your car, but some Cadys/Buicks have extra special CCM (I think Computer Convenience Module?) that controls many of the options and cause wonky symptoms when going south (though I can't believe they'd include the glovebox light on it). In any case check around for any other lights not working that might give hint of upstream circuit for more burnt fuses.
\'96SS SOB: SSRI, Herter Tune, Tri-Y II, , 3000 Edge, F/HO bars, METCO extendeds with CV MMC, Bilsteins, currently Vredestein Ultrac Sessanta (315/35 rear). Finally, wait for it... LT-4 knock module!
\'96FWB BUW-Butt Ugly White: PCMPerformance tune, HDFA w/ swissed filter, 1/2 SLP s.s. catback with H- and Flow Super 50s, oem opti rebuilt 3 times, SS Bars, METCO LCA, Airlift 1000, Monroe SS, PowerTrax No-Slip, CTS wheels with +1 rubber. Finally, yes again... LT-4 knock module!