Blinker continues clicking when turn signals are off

I had the same problem with a 2000 Blazer. It turned out to be a failing multifunction switch (turn signal, cruise control, wipers, etc). It’s a known problem with GM vehicles of this era.

Try spraying some CRC Electrical Contact Cleaner into the base of the switch at the steering column to clean the switch contacts. This only worked for a few days on the Blazer, but at least confirmed the switch was the problem.

Ed B.