Gets my vote, too. It’s more of a boogie-woogie version, though.
It kind of follows “Because My Baby Don’t Mean Maybe Now”
I played it for my wife, who is the jazzmaster in this house and she also identified it as “Frim Fram Sauce”.
My related bona fides don’t really matter, so I omitted them before, but FWIW I’m a jazz singer who has been deep into the Great American Songbook — and active in the DC jazz scene — for the past 13 years. 
I’m actually 100% sure that I’m correct, but was allowing for the chance that there’s a song I don’t know yet that sounds exactly like “Frim-Fram Sauce” but isn’t. Because that’s not impossible…
Nevermind
It’s still bouncing around my head and I’m getting everything from Don’t Fence Me In, to Nice Work If You Can Get It. I gotta find me a new earworm.
With shifafa on the side?
Spellings vary, but indeed.
Yeah, I’ve heard it as “shi-bumpa”.
That’s it! Thanks!
~Max
You’re welcome! And you were spot on when you said “I have a vague feeling the lyrics have made up words about some mundane thing. Not scat, but like a few nonsense words.”
It sounds only vaguely like the version of “Frim Fram Sauce” that I’m familiar with, but then, maybe the version I’ve heard is just an unusual arrangement.
Oh, and I added [solved] to the title.
It also reminds me of this tune (Groove Merchant) :-
