William Taylor Elmore was born on June 9, 1873, in Charleston, Mississippi, to Albert Rhett Elmore and Alexina Jessie Taylor. His father earned a living as a farmer. The family moved to Alachua County, Florida, in the 1870s, and he grew up and attended school there. By 1900, he was working as an office clerk in Jacksonville, Florida. He earned his medical degree from the University of the South in 1904, and he interned at the Willard Parker Hospital in New York City. He eventually returned to Jacksonville and became superintendent of the Duval County Hospital.
He served in the Medical Corps during World War I and World War II, eventually earning the rank of major. He also served as a medical officer in the Florida National Guard. He apparently never married, and he died of a heart attack in Lake City, Florida, on August 7, 1949.