Ditto on BOTH.
I had the same "Click" and it was a the Speedo cable, ( Easy replacement )
But I like the idea of the turn signal Relay.
So the first thing i would do is pull the fuze for the signal as prevouisly stated,
drive it and see if it still clicks,
If So, install the fuse. Pull the cluster and unplug the speedo, (4) scrwes on the dash and a simplle swist of the cable on the back of the cluster.
Again drive it and see if it still clicks, Should be able to tell. if not you might pull the cable from the case and then drive it. this will completly eliminate the cable.
CAUTION !!! I dont know if pulling the cable from the case will leak oil. Meaning the oil level is above that point in the case. Im sure if its not, it will leak a little while test driving but shouldnt leak much.
Be sure to re-install the cable back onto the case regardless to seal until repaired.
Chime in her guys if I got something wrong, I dont think I did But Hey one never knows.