Jay,
The clicking is being emitted by a electro-mechanical relay designed to sound like the old plug-in turn signal relay. The clever ******** also increase the speed of the flashing signal and the clicking noise just like they did when operated by the plug-in turn signal relay if one of the lamps is burned out. But it is actually being controlled by the FCM. But to answer your question, after removing the cluster panel you should beable to "foam" the the relay little speaker slots.
² Turn Signal-On Input - Each time the cluster
detects a turn signal-on input from the turn signal
switch circuitry of the multi-function switch on the
turn/hazard switch mux circuit, the requested turn
signal lamps and turn signal indicator will be flashed
on and off, and an electromechanical relay soldered
onto the cluster electronic circuit board will produce
a clicking sound to emulate a conventional turn signal
flasher. The turn signals and the turn signal
indicators continue to flash on and off until the cluster
receives a turn signal-off input from the multifunction
switch, or until the ignition switch is turned
to the Off position, whichever occurs first. The
instrument cluster also sends an electronic message
to the FCM over the PCI data bus, and the FCM
flashes the appropriate exterior turn signal lamps. If
the FCM detects an inoperative turn signal circuit, it
increases the flash rate for the remaining operative
turn signals and sends an electronic message to the
instrument cluster. The instrument cluster then
increases the flash rate of the turn signal indicator
and the clicking rate of the electromechanical relay
to provide an indication of the problem to the vehicle
operator.
Good luck...