The wiring for the adapter 4 pole to 7 pole and 4 pole item c57674 is wired as followsthe white wire is grounded to the vehicle frame as you have indicated. Occasionally the cables will cross.

Curt T Connector Vehicle Wiring Harness For Factory Tow
Curt 7 way plug wiring diagram. Tm park light green battery feed black rt right turnbrake light brown lt left turnbrake light red s trailer electric brakes blue gd ground white a accessory yellow this is the most common standard wiring scheme for rv plugs and the one used by major auto manufacturers today. The yellow wire is the center pole of the 7 way connector and is normally used for connection to the reverse light circuit. 7 way plugs and sockets are typically used on larger trailers for heavy duty towing such as on gooseneck and 5th wheel trailers as well as larger utility trailers and boat trailers. Like a t connector an original equipment wiring harness plugs into the uscar socket without any cutting splicing or soldering required and it provides a standard trailer wiring output such as a 4 way flat or 7 way rv blade. It can transfer power better therefore the connector is suggested for higher level electric in the auto. Here is the diagram for 7 pin connector.
Curt 7 way connectors are designed to supply power to the trailers taillights turn signals brake lights electric trailer brakes reverse lights auxiliary power and ground connection. This curt 7 way trailer wiring diagram model is much more suitable for sophisticated trailers and rvs. Select vehicles come with a standardized uscar socket that provides a connection point for a curt oe wiring harness. According to earlier the traces in a 7 way plug wiring diagram represents wires. White pin to your ground. 7 way plug wiring diagram standard wiring post purpose wire color.
But it does not imply link between the wires. Injunction of 2 wires is usually indicated by black dot to the junction of 2 lines.