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The third brake light is powered from a dedicated circuit from the brake switch rather than through a relay. Replace the fuse that blew and reinstall the relay and verify that all other lights do still work.
Start by checking the orange wire at the brake switch and make sure it has power, this comes from the stop lamp fuse in the power distribution center under the hood.
If that power feed is ok then press the brake pedal with the switch plugged in and make sure there is power on the white wire leaving the switch. If there is no power then you have a bad brake switch.
If power there is ok then go to the fuse labeled VECHMSL in the box under the hood and make sure it isn't blown, if ok make sure it has power on it with the brake pressed. If there is no power but there was power on the white wire at the brake switch then the wire is open in between.
If you do find power at the fuse then the next step would be to check for power and ground at the third brake lamp. Power leaves this fuse and goes to the lamp, if you're missing power and it was ok at the fuse then the circuit is open in between.
If you have power at the lamp but no ground then you have an open ground circuit or the ground is ground itself is corroded, off or loose.