1998 Chevrolet Monte Carlo brake lights do not

did you check all your fuses

the bulbs have 2 filiments,one for brake one for tail light. check bulbs if they good your swich is bad

IF BULBS ARE OK, BAD TURN SIGNAL SWITCH

This is a common GM specific problem. Your turn signal switch contains an elaborate networking device that has to cancel brakelights while running a turn light. Often times the ground within the turn signal switch is lost causing your situation. After investigating such other possibilities as fuses and loose grounds it may become necessary to replace the turn signal switch. Thank you, Dana

check fuses

The 3rd brake light working does reveal that the fuse is good, and the brake switch is good. Check the bulbs, sockets, and the wiring between the brake lights

Turn signal switch. With you foot on the brake have someone stand behind the car. Wiggle the turn signal lever and see if the the brake lights flicker.

It could be wiring, a bad ground, a defective plug to the tail-light, the tail-light itself, a loose fuse, or a dirty or faulty connection at the hazard switch. If it is the hazard switch you can try to actuate it (on and off) 6 to 12 times. This may help clean off the contacts and let the brake lights, return to normal.

There is only one brake light switch. There should be a wiring harness connector somwhere in the back of the car. Follow the wires from the tail lights until you get to this connector. Take it apart and clean the terminals and reassembl. If this does not do it, move further up the harness until you next connector, do the same thing.

Good luck

I have the same problem,it's the switch inside the turn signal assembly.Unfortunately the entire assembly switch and all has to be replaced.
Hope this helps.