One CMP I have did have a much smaller trailer lighting socket than the one above. The small socket had only 2 electrical contacts inside. This is reasonable if the return path is through the housing of the connector because CMP trailers usually did not use electric brakes. The only wiring would be for tail lights and brake light.
I believe I have a document showing the setup for CMP trailers but will not be able to look at it until tonight.
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