There are two or three versions of this song by Tommy. 'Classical Gas' is not a song I particularly like although I do like the version he does in the video I watched
https://www.youtube.com/watch?v=TQJ1k2HMoRUBeing able to use a thumbpick like a flatpicker uses a flat pick is something that should be easy but tends to be difficult for some. I know I never got good at it. Chet, of course, could do it flawlessly too and seasoned players (Bresh comes to mind) can do it so it's not like it is a secret.
Any guitar technique is attainable...
...if you are willing to isolate it, figure out what is required to achieve it and apply the time (and often monotonous) practice until your eye, hand and mind allow it to happen.
It's like when we learned to get something like the "independent thumb" It seemed impossible for months until one day it stars to kick in.
Isolate what you want to do. Do it SLOWLY until it balances and gradually increase your speed. There are no shortcuts.
Having said that, some folks who have the technique down may propose tips...wrist angle, holding the pick, etc. but it still boils down to play it right slowly before you try to play it up to speed.