Many thanks for the video link, Kmrumedy; I first saw this commercial a few days ago, and almost jumped out of my seat! (I have a black '66 base-model 'Cuda.)
A few things I noticed:
(1) All emblems seem to have been removed, Photoshopped out, or papered/taped over. Take a look at the close-up sequence with our Captain seated in the car: Under the passenger-side vent window, I swear I see a piece of flat-black paper that has been crudely taped over the "Barracuda" script emblem. See if you agree!
(2) To me, as to many of us, it's "obvious" the car is a 'Cuda (can't decide if it's a '64 or '65, though, or to what extent it may have been customized), but it's probably not a Formula S. That's because the inside rear-view mirror doesn't have the "day/night" toggle lever. 'Cuda wonks know that the base-model cars got non-switchable mirrors with stainless-steel backs; the Formula S items have the toggle at the bottom, and a black crinkle-finish back.