In context like He began to play fatback/swing-based R&B

It's a style of drumming. The only example I can think of was in an arrangement by Waldo de los Rios of the Haydn Toy Symphony, second movement.

Uhhhm. Thank you.

You make it sound like I gave you either an incorrect or inappropriate response. I didn't say it was a great example. I just said it was an example. Waldo de los Rios did contemporary arrangements of classical pieces (among other things), thus fatback and Haydn. That the drumming was called "fatback" was pointed out to me by a friend who was not only a professional drummer (who also played with the Saskatoon Symphony) but a veterinary medicine major (it was during my college days).

So it all makes sense! I think a "fatback" is some sort of a drum style where you sweep with your drumstick over the drum, while playing. Like rubbing the back of a pig.

Reverend Jim, now you are wrong. I liked your reply (about drumming style).
I came across this word here:

His tenor sax solos were searing, harsh, and unrelenting, played with a vivid intensity. But in the '70s, Shepp employed a fatback/swing-based R&B approach, and in the '80s he mixed straight bebop, ballads, and blues pieces displaying little of the fury and fire from his earlier days.

I may not have provided the definitions of all the uses of the term fatback but the one I gave was correct and was correctly described by ddanbe above.