I think that the brake lamp turns when there a difference between resistance between the bulbs is detected by a sensor on the driver's side tail light. You should download that shop manual and clean the appropriate grounds. G551 and G501. Those are in the trunk. The shop manual will show those locations.

You may want to remove the brake bulbs and make sure there is no corrosion on the connectors or that the bulbs are not loose.

 

If you download the manual PAH referred to, you can get specs on the sensor and check sensor resistance is in spec. If it measures open or dead short, it's bad.

good luck