Im posting this because I had the problem with 2001 f150 lariet with boat trailer brakes locking up when I tried to back up...after searching thread after thread I got no answer because everyone was over thinking the problem....
I finally got out the owners manual and studied the fuse diagrams...problem solved...
In the fuse panel under the hood I found there is a spot for a reverse light relay that sends power to the center pin of the 7 pin plug...mine was missing...
Hope this helps somebody...

 

You should explain the rest of the story:
Your boat trailer has surge brakes. When you back up, the surge brakes activate causing the lockup. Your boat trailer has an electrical lockout solenoid that is in series with the brake line out of the surge brake master cylinder. The lockout solenoid is turned on by the Reverse pin in the trailer socket. When you put the truck in reverse, the pin goes high turning on the lockout solenoid which closes. This closing prevents brake fluid from the surge master cylinder from going to the trailer wheel cylinders thus allowing you to back up.
Take the truck out of reverse, the pin goes low and the valve opens allowing the surge brakes to work again.

 

Just wanted to add another possibility for the surge brakes locking up when reversing. I ended up installing a brake controller in my new 2022 Lariat and to verify that it was working, I moved the gain around and it showed that I had moved it down to level 7. I had at this point never towed anything with the truck. I use an adapter plug on my 7/4 wiring connector to convert to 5 pin. I pulled my pontoon boat out for the season and when I went to back up, the surge brakes locked up. I did the manual override on the surge brake to get it to back up. Did some troubleshooting and found that the voltage on pin 5 that turns on the brake solenoid (the brake solenoid in the case of surge brakes disables the braking in reverse) was only around 9 volts. Turned up the gain on the brake controller from 7 to 10 and the voltage on pin 5 went up over 13 volts with the truck running. The solenoid needs around 12 volts or more to disable the brake in reverse.