A clicking noise may be noted from the turn signal flasher after the turn signals are switched off. This is commonly cause by a faulty turn signal switch which will require replacement.
Car Problem Reports
GMC Sierra 2500 Turn Signal Switch May Fail and Cause Clicking Noise
GMC Sierra 2500 Problem
Average Mileage: 131,000 mi (70,000 mi - 183,000 mi)
Visitor, 1999 GMC Sierra 2500, 140,000 mi
Same problem. Stops clicking when brake is depressed.