Ray Grismer got the Rhythm Count concept rolling by developing the core idea, and then showing it around to other magicians in the early 1980s. One of these magicians was Larry Jennings, who went on to publish two false displays in A Visit with Larry Jennings, 1982, p. 1 & p. 5. The first display was a straightforward combination of the Flushtration Count and Olram Subtlety that Larry dubbed the “Double Olram”. The second display was much closer to what is now referred to as the Rhythm Count. The display was christened with its current name in The Classic Magic of Larry Jennings, 1986, p. 186. Jennings never mentioned Grismer's name in connection with the concept.
Allan Ackerman—another of the early magicians who Grismer showed his original display to—gives a brief overview of Grismer's technique in the introduction to his own Fingertip Rhythm Count in Classic Handlings, 1999, p. 14.
Before Grismer and Jennings, Karl Fulves explored the idea of a false display in which both hands alternately display cards in a small packet. The faces of two cards are shown twice and appear to make up a four-card packet. See “The GIT-M Move” in Interlocutor, No. 16, c. 1978, p. 59.