My son had the same problem on his 1995 Monte Carlo. The brake light in rear window worked , as did the tail lights and emergency flasher but no brake lights came on when pushing the brake pedal. Anyway , the problem was in the turn signal switch. This involved taking the steering wheel and column apart , taking the airbag out ( careully ) and it was more than I wanted to handle. The mechanic charged 227.00 including part and labor. .
Check the switch on the brake pedal
brake light switch would be most common cause
Possible ground issue at the taillights.
BAD BRAKE LIGHT SWITCH AT TOP OF BRAKE PEDAL
More than likely it is the brake light switch that is attached to the brake pedal.
The BOO (Brake On/Off) Switch may need to be replaced. If it is bad, it would cause the brake lights to NOT illuminate when the brake pedal is applied.
Check your brake light switch at hte brake pedal.
brake switch located on the top of the brake pedal
The most likely cause is a bad brake light switch (if none of the brake lights illuminate) but if its only one of the brake lights, try changing the bulb. Even if they still work as running or turn lights because they have a double filament and may still work partially, but not as brake lights.
Check the switch adjustment on the brake pedal arm.
Blown fuse, bulb, or bad brake light switch.