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If both the outside and hatch are supposed to have brake (stop) lights (so four stop light bulbs would be on when the brake pedal is pressed), and that doesn't happen, that's the path I would follow to troubleshoot.
Given the condition of the socket on the left, I'd start by checking the others, and replacing the remaining brake/tail bulbs.
The left corner and left hatch seem to be working properly, but not on the right. When the brake pedal is pressed, why would the right hatch tail light filament be on if the lights are Off? I suspect the right corner -- it could have a corroded connector or a bad bulb, especially a broken filament crossing over internally to the other filament in the same bulb so that when the brake is pressed, power is going to the tail light circuit.
Given the condition of the socket on the left, I'd start by checking the others, and replacing the remaining brake/tail bulbs.
