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.Google+
Car Problem Reports
Chevrolet Tahoe Turn Signal Switch May Fail and Cause Clicking Noise
Chevrolet Tahoe Problem
Average Mileage: 161,692 mi (90,000 mi - 208,000 mi)
Visitor, 1999 Chevrolet Tahoe, 172,538 mi
blinker relay will not stop clicking even when blinkers aren't in use.
Visitor, 1999 Chevrolet Tahoe, 200,000 mi
turn signal switch makes noise even when signals are not on.
Visitor, 1999 Chevrolet Tahoe, 90,000 mi
blinker clicking noise randomly continues or comes on when blinkers are not activated. Also electrical buzzing noise from column periodically.
Visitor, 2000 Chevrolet Tahoe, 155,000 mi
Flasher Relay "clicks" when signals not on.