96 chevy blazer

heres the deal, my 3rd brake light (CHMSL) is not working, i checked the fuse, and thats not the problem, so i next went to check the actual light. this is where i ran into my problem

one of the screws that fastens the light console to the car wont come out. the screw just spins around, both left and right. the screw is "counter-sunk" into the console, so i dont think i could cut off the head of the screw. does anyone know any way to fix this problem?

 

Drill through the screw and re tap the whole.