According to Barlow's book The Vanishing American Outhouse:

"Vents often doubled as symbols for gender identification.  Luna, the
ancient crescent shaped figure, was a universal symbol for womankind.  A
moon, sawed into a privy door, served as the "Ladies Room" sign of early
innkeeping days.  Sol, a sunburst pattern, was cut into the men's side of
the outhouse.  These symbols were necessary because in Colonial times only a
fraction of our population could read or write."

page 4.

While "popular," Ron Barlow's book (1992, Windmill Publishing Company, El
Cajon, CA) is an invaluable aid for the privyologist.