What’s the exact process to identify a real 66 Formula S Barracuda?

You could definitely order almost anything, if not everything, separately from the Formula S package, it is clearly stated, especially in the 69 info.
Formula S emblems not available outside the S package.
150 speedo could be ordered independent of the Sport Package.

Imo, no way is it less of a car, it as unique as the owner who ordered it, and probably didn't want to pay extra for items that added nothing to performance or driveability, and added to the monthly payment.

In the late 80s early 90s my car had the fenders replaced with rust free ones and minor repairs to the lower rear quarters before it's only respray.
I know because I talked to the second owner multiple times, and I bought it from the third who never registered it.

So in 67 the only Formula S exterior identification was the emblem on the fenders, and used fenders bolted on obviously doesn't mean it's not an S. (unless 383, then 383 emblems and dual exhaust valence)

Stuff happens, and finding a set of rust free fenders at that time was probably an easier endeavor, may have even initiated a respray.

Formula S emblems, and 383 emblems, were never put back on, the V Eight emblems were left on, possibly on purpose.

Ironically, when I joined this forum I returned those emblems which led to comments such as, that seems to have grown some emblems since the last time a pic was posted.