All that can presently (November 2023) be gleaned about
John & Mae Burke from sheet music covers and by Internet searching is that they were presumably an American vaudeville act that have been featured on 2 works published between 1914 and 1916.
Their portrait on the left is taken from
Cumberland (1916) words & music by
Halsey K. Mohr, and published by
Shapiro, Bernstein & Co., New York & Chicago, USA.
Surfers are welcome to contribute any further information about these performers.