The flasher you might have found while looking at the swingout Convenience Center panel would be the hazard flasher. Note the silver can:
The flasher for the turn signals is tucked up under the dash in the driver's footwell area. GM engineers must have had a ball playing "hide the component" with this item. There is a steel spring clip affixed to the lower edge of the dash panel. You'll have to remove the lower trim panels and covers for the HVAC ductwork. Reach backward at the lower edge and you should be able to feel it, or look with a good light and a mirror to view it. Are we having fun yet?