The reply button is not working, so I post a response this way.
It sounds like the multifunction switch (turn signal, wipers, cruise) is the problem. When the multifunction switch failed on my 2000 Blazer the flasher unit behind the glove box was on continuously. The clicking was constant whether or not the turn signals were on or off.
Try spraying some CRC Electrical Contact Cleaner (try Lowes or Home Depot) into the base of the switch on the steering column to clean the contacts. This stopped the clicking on my Blazer for a few days but I had to replace the switch.
The switch was ~$200 and figure on a few hours of labor for installation. Verify the switch is bad since it’s not a cheap fix.
Ed