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.
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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