First thing I would look at are the female connectors and make sure they are touching each other. By that I mean to themselves NOT each other! If they do not make good contact to the trucks male pins this will give you the issue you are seeing.
Had the same thing on my Ram, the Rv dealer was pointing his finger at the truck but when I bent each of the trailer connectors the problem went away. Not saying the truck is not the issue but I would try and bend both sides of each of the tabs and see if the problem goes away. If it doesn't then have Ford replace the plug on the truck.
Hope this helps Don