Yeah - some people actually want to turn right when towing! Using the factory connector plug, I could only turn left, otherwise the cable would pull out. Started getting real dizzy. Plus, it's a pain to reach under the rear of the vehicle every time to plug / unplug the cable - you'll understand when you're old and have bad knees.
Anyhow, the only 7-pin extension cable I could find was for 5th-wheelers and was way too long, and I really didn't want a 5 foot slinky hanging under the rear of the vehicle. So, I took the 7-pin connector left over from the former tow vehicle, got a new trailer-end plug, and made an extension pigtail. Now I have the 7-pin, plus the 4-pin, plus a place to mount the 2-conductor connector for the rear-view camera on the back of the trailer, plus a bunch of fancy high-tech flashing red LEDs. Maybe lost a little bit of departure angle, but not too bad. The mount is just a piece of flat stock with 3 holes in it - doesn't get much simpler than that - and a couple of dabs of RTV on the bolt head to keep it from working loose. The heads of the 1/4" bolts snug up against the front edge of the bumper plastic, so it doesn't twist even though it's only mounted using the single bumper cover bolt. There's not too much load on it anyhow. It's semi-permanently mounted to the factory connector using a few wire-ties.
The pieces of slit black nylon tubing work nicely to keep the safety chains from chipping the paint off the hitch and allowing rust to get started. The hose clamps keep the chain hooks positioned on the tubing. Looks kind of dumb, but it works - and it looks better than rust.