Yes, it will! With the 6-way installed you can use the included cord to connect it with the 7-Way on your RV. This adapter cord connects your RV to your towed car with a 7-way plug on one end and a 6-way on the other.
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Roadmaster Bulb and Socket Tail Light Wiring Kit w/ 7-Way to 6-Way Adapter|57614
This complete kit includes everything you need to display brake and turn signals on your towed car. Bright LEDs mount inside your vehicle’s tail light housings, with the wiring out of sight. Includes 7-to-6-wire adapter cable and 6-wire socket.