Chevy Trailer wiring harness

I bought a used 2010 Chevy Silverado Crew a couple months back. We picked the boat up in mid May and towed it to the lake and due to weather and moving hadn't had a time to use it till this last week. What I found when I tried to back up was that the lock out solenoid wasn't engaging and the brakes would lock up. Luckily I had the emergency key thing and just used that so we were able to launch and use the boat. I didn't have the right tools at the lake so had to wait till we got home yesterday to look at it. The truck appears to have a after market harness, but I'm not 100% sure as I bought it used. Guessing that because my brothers new 13 with factory tow just has the 7 round and mine has a 7 round with a 4 flat on the side. When I tested it at the truck side plug I have running lights, brake lights, turn signals, but no power on the reverse lock out/light pin. Looking at the plug(on the truck) I believe that should be the lower left pin/spade. I came to that conclusion as thats the only pin/spade in the trailer side plug I don't account for with running, left turn, right turn, brake. Also am I correct the center is the ground?

I guess the question is should a standard plug be wired for the reverse light pin? Or is this something I have to add? Can I just pull a tail light and tie into the reverse light and run it to the correct pin?