The first description of this trick was in 1729, in a book from Japan: the second volume of Tawaguregusa (“Book of Games”) by Kiyu. It's name there was 通い玉 Kayoidama: loosely, “back-and-forth balls,” referring to the spherical beads on the ends of the cords. (For further information, see Max Maven's “Tracking Slum Magic to Its Lair” in Gibecière, Vol. 14 No. 2, Summer 2019, p. 165.) There is no evidence that knowledge of the trick traveled outside Japan.
A remarkable example of independent reinvention appears to have occurred roughly 180 years later in England. Around 1912, Chris Van Bern created a pocket version of the trick, which he called the Rod and Beads. 1912 is an approximation based on a comment in a letter by John B. Ward, paraphrased by Brunel White in the July 30, 1938, issue of The World’s Fair (p. 12).
In 1927, Will Goldston published the trick, under the title “A String Problem”, in Further Exclusive Magical Secrets. Goldston begins the write-up with: “For the secret of this ingenious little trick I am indebted to Mr. William Jeffrey.” This is the only link between the trick and Jeffrey, and Goldston's wording is vague, suggesting that he may have learned the method from Jeffrey, but was not claiming its invention was his. The source of the trick could well have been Van Bern. Twelve years later, Goldston was advertising the trick under the title “The Bamboo Rod”; see Goldston's Magical Quarterly, Vol. 5 No. 3, June 1939, inner front cover.
The trick was first marketed circa 1935 as the “Mystic Rod and Beads” (see The Magic Circular, Vol. 30 No. 335, November 1935, p. 28), and all subsequent mentions credited Van Bern with its invention.
When Louis Histed published his version of the trick, “Papyrus”, he wrote, “I originally saw Chris Van Bern perform the Rod and Beads many years ago, about ten years before it came on the market in this country. It is reputed to be very ancient, but although I gave some thought to the problem I don't think I succeeded in discovering the principle. The method which I give here for achieving a similar effect was soon discovered. Later, I found that that prolific inventor Tom Sellers had been struck by exactly the same idea. Fairly recently I bought a bound volume of his collected works, and I find that he describes the effect almost exactly as set down here.” (See The Magic of Louis S. Histed, 1947, p. 55.) Tom Sellers's method, mentioned by Histed, was published as “Rod and Strings” in Immediate Magic, p. 13, in 1937.
Circa 1938, Abbott's Magic Novelty Co. seemingly reduced the size of the prop from that commonly manufactured to a pocket version, making it presumably nearer the original Van Bern model. Abbott's called it the “Devil Stick” (see Tops, Vol. 4 No. 1, Jan. 1939, p. 57). This prop did not break apart in the middle to prove a lack of connection between the cords. Instead, it was passed for inspection at the end, and failed to work as it had in the magician's hands.
Assuming that Histed knew nothing of the Japanese origin of the trick, he may have been referring to “Solomon's Pillars” when he mentioned that the trick “is reputed to be very ancient”. “Solomon's Pillars” (dating back to the 1600s) consists of two sticks, joined at one end and with a cord apparently strung through the opposite end. The cord is seemingly cut between the sticks, and then restored. This trick and the similar “Nose Bridle” (see Reginald Scot's Discoverie of Witchcraft, 1584, p. 351) seem to have been the simple parents of the more deceptive Chinese Sticks and Pom-pom Prayer Stick.