The brake light bulbs are all good, though two of the lights are not working. I'm thinking it is either the fuse, or connector is damaged.
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Your suspicions about the connector being faulty would be supported by your symptoms, but a blown fuse would result in none of the brake lights working. I would suggest having a certified mechanic like one from YourMechanic inspect your brake lights by testing for voltage at the connector, and working backwards to power.
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