Your 2006 Chevrolet Suburban has and LED third brake light assembly, the bulbs are not replaceable. You must replace the complete light assembly. Make sure to check for proper power and ground to the light assembly before running off to purchase a new light!
We have the same problem with the brake light and also the rear door hatch doesn't lock! Was told by mechanic they would have to check the entire length of wire from the front of the vehicle to the back. This apparently requires removing the headliner to get to the wires.. is this true or could it be some type of fuse or sensor?