What "makes" a 66 Barracuda a Formula S ??

That's all good stuff but there are limited identifiers on the car to prove you have one after 58 years unless you're the original owner or there's a paper trail of sorts..
exactly.

if i was in the market for an S car i'd 100% want a paper trail. it would be entirely feasible to fabricate one out of thin air with the right sets of parts.