There are some switch boxes behind the glove box and radio. The switches can break and make clicking noise when trying to open or close. It could be faulty and not staying open. Or it could be something in the AC controls.
Have you tried disconnecting the battery for about fifteen minutes and resetting everything. That might get things back on track and it's free.
chevy runs deep, Don't step in chevy!
289 - Holley 4150 570cfm; Performer intake; mild cam; MSD HEI; 302 heads; Roller Tips; Hedman Tri-Y headers; H-pipe w/Flowmaster 40's; 9 in posi 3.50; 205/50-17F; 225/50-17R.