I'm not a very physical performer, but, I've noticed that as I get older, I sway more, especially when playing mouth organ. Intricate instrumental pieces that require more concentration probably inhibit movement in the player, this happens with Irish music too.

Mutter Slater, the flute player of the eccentric English band of yore, Stackridge, used to sway profusely while playing, not to the rhythm of the tune, but possibly to some innate internal rhythm of his own. It was the same cadence, whatever the speed of the music. I 've noticed this with a number of players over the years (and some dancers).