The right brake light on a 97 Cutlass Supreme works only part of the time. The bulbs have been replaced. It’s a two filament bulb. The same bulb is used for both the tail light, turn signals, and brake lights. The tail light and the turn signals both work fine. The turn signal uses the same filament as the brake light. The left and top center brake lights appear to be working properly. Would a faulty brake light switch result in only one brake light not operating, or is there something else to look for?
The switch is probably an all or none thing. My guess is a corroded connection in the bulb socket, if you have a voltmeter you can try to find the bad connection, it could be a power or ground problem.
I have seen this problem numerous times, and you are probably not going to believe the solution. This era of Grand Prix/Cutlass/Luminas had a problem with the turn signal/multifunction switch. The brake light circuits are run through the turn signal switch in the steering column, and when the switch gets worn out it will cause one or both of the brake lights to cease functioning. The turn signals will continue to work fine, and the third brake light will not be affected at all. I have replaced about a dozen of them in the last five years and seen countless others running around with only a third brake light working.