The video is exactly what I'm experiencing. Ford would not cover this even though the video shows the problem exists without any mods. In my case I had BMR A arms and a bump steer kit so Ford used its typical "car has been modded so we can't cover it".
I have noticed that the vibration only occurs when external temp is above 75F so I believe the under hood temps contribute to a hot steering gear and box which causes the vibration. Before spending any money on a manual steering box I am going to vent the hood this fall/winter.
2011 GT CS MT
JLT CAI/93 tune, Alum DS
Rear seat delete