The BCM controls the turn signal indicator lights over the Serial Data Bus. The flasher that turns the signal lights ON/OFF is located in the BCM, but the "clicker" is in the instrument cluster. It is probably mounted on the logic board. Haven't yet found out how the clicker is powered/controlled.
The turn signal sound comes from a speaker that is soldered to the back of the instrument cluster. To replace it you have to find one from another cluster as this part is not available as a single unit. If you want a softer sound one from a Pontiac G6 will work with some modification .
Go to "Account Details" under your name at the top of the page, then click on "Update Settings" on the left of the page. At the very bottom, look for "Software Verification" and uncheck that box if it is checked. Then log out and log back in. That should solve the problem.