Looking at the linked wiring diagram, trailers that are required to have a trailer breakaway system need 12 V power on pin 6 to keep the system’s 12 V battery charged. When the trailer breaks away, this 12 V battery applies the electric trailer brakes.Yup, this is correct, per this article from @rypalmer above. Trailer Wiring Diagram – Lights, Brakes, Routing, Wires & Connectors
Perhaps this is leading to some of the confusion about the need for 12 V aux power on pin 6 for trailers with brakes. Trailers without a breakaway system don’t need it, and use pin 5 to control and activate their electric brakes, but trailers that also have a breakaway system need to have both pin 5 and pin 6 functional.