I suspect that on girls, people were using Elisha (pronouncing it "eh-LEESH-uh") as just another corruption of Alicia, along the lines of Alisha, Aleesha etc - probably not connecting it to the male Biblical name.
Again, the male and female names Jan are separate (although not unrelated: both are forms of John).
It's not quite the same thing, but from the 1100s to the 1400s, Julian was one of the most popular girls' names in England, being the Anglicized form of Latin Juliana. Julian on a male was not found until the 1200s, and was less common. So in this particular form, it was used on females first. Then, as happens with all names, it went out of fashion for both genders. When revived in the 1700s, Julian was used mainly for males, and the variant Gillian for females: occasionally Juliana as a learned form. So if you're looking for a name that was female to male, then Julian is one ... See Withycombe for detailed analysis of this.