Thanks for writing. It's flattering to me that this is of interest to you.
The authorship is no mystery. I don't know of any time it's been recorded or in print and not been attributed to me. It's in ASCAP's database, etc. I even registered the copyright with the Copyright Office in the early 70s when we first recorded it. These are the usual tracking systems set up for those purposes.
I hope it won't disappoint you if I tell you the honest truth, which is, as a lifetime New Yorker (either NY City or Ithaca, NY where I composed the tune), I used to think of the armadillo as a comedy animal. Never had seen one (still haven't, strange but true, though I've now been in different parts of Texas, many times), and thought they looked funny in pictures and just thought the word sounded funny. As another example, in my Bluegrass Banjo instruction book, when I needed to supply verses for She'll Be Coming Round the Mountain, I put in there, "She will kiss an armadillo when she comes..."
So that's where the name came from, a guy in his early 20s at a loss for a name for one of his first original tunes, thinking of a "funny" name, and that's IT.
If you are interested in how the tune itself came about, it was a spinoff of the steel guitar tune Remington Ride, which was done on the banjo by Don Reno. I added the bridge using the simple but slightly unique chord progression of F G F D (assuming the key of G), and that was that. A very simple tune. Its long life I attribute to how darned easy it is to learn, while still being just a bit off the beaten track, and using the attractive sound of the F to D chord change.
That may be more lengthy than you imagined was the "real story", as well as more boring, but there it is, the unvarnished truth. Nothing to do with Texas, or even armadillos, unfortunately.
But I still like to play it and improvise on it, since I still like the chord progression. I hope you enjoy it too. I have never heard it as a solo fiddle or guitar piece, but I'd like to.
Thanks for writing,