I have same year Tahoe and same problem. Check fuses first to make sure it isn't a fuse. The third brake light assembly can be removed by opening the back door and unscrewing the screws. Then unplug the connector. A new unit is about $175.00 and the whole unit must be replacee as it is LED light not bulbs.
Yes they indeed have brake lights...
How do you replace a break light switch on 1995 Chevy Tahoe
BEHIND THE BRAKE PEDAL
about 3 dollars
3rd brake light or rear brake lights?
If your brakes lights are not working and all of your other lights are OK try replacing your "brake stop switch". You may have to have either your local auto shop or local dealer replace the switch because it's hard to do yourself. I had the same problem on my Tahoe and replacing the brake stop switch solved it right away.
either dimmer switch or blown fuse If you are saying that the tail brake lights are working but the third brake light is not....It may be a defective turn signal switch in the steering column.
Start with checking the fuses and bulbs. See sources and related links below for bulb information.
On the junction panel on the firewall just above and left of the brake pedal. You can see it quite easily, pulls out. Replace with exact part or lights flash at the wrong rate.
When you open your tailgate...are there 2 screws near the tail-light? homshopper at yahoo dot com.
The brake light switch is bad, look on top of the brake pedal under the dash and you will see the switch, replace it and you will have brake lights.
I have a 97 Tahoe and the brake lights were not working and the problem was in the emergency flasher switch. I just jiggled it and the brake lights worked so am thinking you might have the same problem. It could also be the brake pedal switch located right on the pedal arm.