Hi, Lynn - I've crosslinked this thread with the threads on "I Points to Myself" because there are similarities, but I dont' think it's the same song. Tom Glazer (On Top of Spaghetti) wrote a book in 1973 called Eye Winker, Tom Tinker, Chin Chopper: Fifty Musical Fingerplays. Here's the title song:

Eye Winker
(melody and new words by Tom Glazer)

Eye winker, Tom Tinker, nose smeller, mouth eater.
Chin chopper, chin chopper, chin chopper, chopper chin.

The head bone, the neck bone, the elbow, the knee bone.
Chin chopper, chin chopper, chin chopper, chopper chin.

The shoulder bone, the wrist bone, the chest bone, the rest bone
Chin chopper, chin chopper, chin chopper, chopper chin.

Eye winker, Tom Tinker, nose smeller, mouth eater.
Chin chopper, chin chopper, chin chopper, chopper chin.

verse 1: Wink eye (or blink both) on eye-winker. Sniff on nose-smeller. Chewing motions with mouth on mouth-eater. Nod head vigorously rest of verse.
Verse 2 & 3: Point to each bone mentioned, and not vigorously on chin-chopper words.

But there's nothing about the kitty sitting. I wonder where that comes from.
-Joe Offer-

https://www.youtube.com/watch?v=f6xZK1j2m98

https://www.youtube.com/watch?v=UOgMu58AV5M