Hi,
Most times it is the socket itself. Remove bulbs and inspect for corrosion or pushed in connection points.
As far as the wiring schematic, I attached the entire exterior lighting schematic below. I had to cut the pics in half to make them readable. In pic 3, I highlighted the brake light on the right side.
Here is a link you may find helpful:
https://www.2carpros.com/articles/how-to-check-wiring
Also, check the ground for that light. It could be corroded or loose. See pic 3 for location.
Let me know what you find or if you have other questions.
Take care and God Bless,
Joe
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Tuesday, March 2nd, 2021 AT 7:55 PM