Back from the dealer. They found wires blocking the CD from loading. Works now. And yes, I still use CDs.

Proudly.
Yes, the liftgate is/was opening on its own. It did it during delivery and the salesman thought we were unknowingly doing it until it did it for him while he was holding both remotes and standing at the side of the truck. When I mentioned it at the service appointment this afternoon, the service advisor looked at me like I was an idiot. When I picked it up she said the liftgate mysteriously opened 3 times for the tech. (Yes, the validation felt good.) They reset the module, or some such thing, and told me to watch for it happening again. If it is still randomly opening, they will need the truck for at least a full day so they can communicate with Ford for a fix. Fingers crossed.
I just learned it was built on a Monday, so I'm planning for a lifetime of problems. Sigh.