How do i replace the light for my third brake light? it's out.

See the link:

1998 Buick LeSabre Center Tail Light Third Brake Light Replacement

The circuit to the taillight brake bulbs goes through the turn signal switch. Sometimes the switch can cause this problem.

Check your fuses if it isn't that check and see if your bulbs are blown.

replace the brake light switch mounted on the bracket by the brake pedal. You need to adjust it to operate correctly also. The third brake light works off a different circuit when applying brakes

It could be the Third Brake Light assembly is bad, remove the assembly and have someone step on the brake and you can check to see if you are getting current to the contacts or wires.

If no power, replace the assembly.

Replace the brake light switch located by the brake pedal. That will resolve your problem

on chrysler products the third brake light is run independant of the body control module, try checking the fuses that run the brake lights and see if any are faulty if not check you have voltage at the switch and a signal getting to the lights.

The third break lights are LED and the circuit board may have gone bad or the solder may have gone bad. The circuit board is built in the third brake light and is a seal unit. You may have to replace the unit, there is a relay for the third brake light and that is located on the glove box behind the panel that say's relays. There are three relays in there, the center is for the fuel pump and the two out side are for the A/C and third brake light. Just swap them around and see if the brake lights come on. Good luck and keep me posted. 

the third brake light requires a wire ribbon replacement,
typically on bentley gt. It is quite the job since the light is installed at the factory before the rear window is put in, There is a procedure for replacement leaving the glass in but requires replacement of the light itself and the ribbon cables,

have you replaced the bulbs?