I can't speak for all never Cessna models, but on the Sovereign, the Master Warning and Master Caution light assemblies do not use bulbs. When the light ceases to work...... the whole thing will have to be replaced.
Two fingernails will pop the light cover off. The actual assembly is held in by two tabs that pull up to a mounting plate that butts up to the backside of the glare-shield panel. These tabs are loosened to the point of swinging back into the switch with two allen head screws.
With the switch removed, the sleeve can be seen. On the rear side of the sleeve, there are two cut out slots that the tabs engage and pull up to for securing the switch assembly.
The switch is held into the socket by two bent tabs. One can be (barely) seen in this image above. A awl or pocket screwdriver will bend these up quite easily.
Switch removed and socket visible.
The sleeve has nothing to back it up when inserting the switch assembly. On this aircraft, removal of the co-pilot's navigation control panel allowed for holding the sleeve in place while the allen screws/tabs are tightened down. (This was rather lucky...... the initial thought was that the glare shield cover was going to need to be pulled up.) It is best practice to screw the tabs as far back as possible before sliding the sleeve over. If they are to far forward they could actually be beyond the sleeve cut out and they will not have anything to catch.
New switch in. Controller out. After a re-install of the controller, it needs a functional check just to be sure all functions operate normal.