The first published telephone test was John Hilliard's “Twentieth Century Telepathy” in The February 1905 Sphinx, Vol. 3 No. 12, p. 150.
Bob Loomis reports finding a description of a second-sight feat performed by Harry Hermon and his wife over the telephone in 1884 or shortly before. Hermon's original relation of the feat is given in his 1884 book, Hellerism: Second-Sight Mystery; also see Loomis's “Phoney!” in The Magic Circular, vol. 108 No. 1175, June 2014, p. 184. Additionally, Bill Kalush has found a reference to Houdini having performed such a routine in the 1890s.
Rufus Steele's Card Tricks You Will Do (1926, p. 22) includes “Mind Reading by Telephone” by Bill Bournau, which has the earliest instance, discovered to date, of coding by including or excluding actions made by the spectator during the call to the medium. This predates Read's “Calostro Act” by six years, and Annemann's “Weird Wire” by twelve.
(See also Mr. Wizard Telephone Test.)