Let try it another way - About how old is/would be your father William Fagot to guess his approximate birthday. Then his father would be about 18 - 20 years older. Try to be about.
I also have a Hugh Edwin Fagot, b. 1881, who had a brother John Albert. Then John Albert had a John Albert, b. 1895 (who did live in FL); a Hugh Louise, b. 1902, and William, b. 1914, among others. Which one would it likely be? Do you have anything that might show a middle initial? A date of death?