The BRP plug is not a "standard" nine-pin. You will not use all the wires...nor does BRP. The Tongue Harness has the wire functions marked. There are two brake light wires. Choose either one unless your trailer has separate brake light wires for each side.
Here is the pinout diagram. You can either cut off the original trailer connector and wire up the BRP harness/connector (or a portion of it), or use it to make an adapter to a 5-pole connector that will match your trailer. If you expect to haul a different trailer someday, you may wish to make the adapter, otherwise wiring the BRP harness directly is the simplest.