Are you sure the bulb is good?
Are you sure it’s seated properly in the socket?
Have you tried spraying the socket with contact cleaner?
Like insightful, I stick a broomstick between the headrest and the brake pedal to keep the lights on while walk back to check. Sliding the seat forward as much as is necessary to press the pedal usually works. The brake light circuits remain “enabled” even when the engine is off, so you do not need to (and should NOT) have the engine running while you do this.
If the ground to the chassis isn’t solid for that bulb connector wiring harness, this can be a symptom. I had this happen – believe it or not – at the DMV, prior to a driving test. It was rather embarrassing. The test guy said I couldn’t take the test b/c my car’s brake lights were too dim. A quick inspection inside the trunk showed the ground had popped loose from its moorings.
On my Pontiac, the car has to be running for the brake lights to work. I like to check them as the garage door is closing but need to make sure I shut the car off right away or bye bye Bing.