I had the exact same issue with the "clicking" continuing afterwards (with no lights flashing). Sometimes it would also click very quickly, and then it would randomly click even when I haven't turned on my turn signals.
Before replacing anything: try spraying electrical contact cleaner in the turn signal stalk. Move the turn signal stalk up and down several times.
I think mine just gets very dirty? Either way, this fixed my issue. The issue returned about 6 months later - repeat - and it hasn't happened again in over 8 months.
Just something for you to try. Super cheap, too!
