have you ever heard the theory of the shaped charge in the back rest of the seat in front of JFK? If not look into it. I think it makes the most since as it was a backup just in case the gun shots did not hit the mark. In the video it appears that the driver leans over and reaches towards the middle console for a possible switch to activate the charge.
you need to find a different version of the film. The one you have is zoomed in and at full size frame 313 you can see both the drivers hands.
here is a better version. pay attention to the final shot. just before the driver leans forward. when the shot goes off the governor is thrown forward by the seat. shaped charges were used in oil fields and mines which fit Bush's knowledge.
https://www.youtube.com/watch?v=jdwVUBlK-Y0