I'm not familiar with your 2002 Gran Prix, but the problem you describe is universal to all vehicles.
The fact that the "third" brake light [in the rear window package tray] IS WORKING, indicates that the brake light switch IS WORKING properly!!!!!
That suggests that the reason that the other two brake lights are not working is that there is an "open" condition in the wiring circuit to the other two brake lights. This is confirmed by the fact you replaced the lamps [bulbs] in those other lamp holders with known good lamps.
There could be several causes for an open circuit, but the most common include:
turn signal switch needs replaced!
How about a malfunctioning brake light switch
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.
I just had my Daewoo Leganza brake light switch replaced. It goes under the brake pedal. and now my brake lights work fine.
The brake lights in your 1983 Nissan pickup truck are controlled by the brake light relay switch. When the brake light relay switch malfunctions the brake lights will stop working.
If none of the brake lights are working i would suspect the brake switch at the brake pedal.
Possible bad switch on the brake pedal? When you push on the brake pedal, it activates a switch, that switch turns on your brake lights. If the bulbs and fuses are ok, check the switch with an ohmeter.
probably the brake light switch on the pedal if none are working at all
Brake switch needs replaced.
try the brake switch on the back of the brake pedal
Probably the flasher unit needs to be replaced. This is an electronic switch which usually mounts underneath the dashboard.
Out of adjustment. Adjust the mounting of the switch so the brakes lights are off until you press the brake pedal.