“Don’t play the piano part. I’m playing that. Don’t listen to me. I’m supposed to be...
Thelonious Monk creates a list of tips for playing a gig
I agree with his first comment about keeping time, and the one you quote about knowing who's following who during a solo.
(When I say "agree", I mean "feel guilty because I don't always follow".)
Monk knew I thing or two, I think ;-)