William's birthplace is noted as Scotland. According to the Chronicles, Fanny Elliott brought her aging father to Ireland, meaning she was old enough to have arranged the journey. The Rutledges are supposed to have come around the "middle of the 18th century", and Fannie coming about two decades later. If William is about the same age as Fanny, then he must have been born in Scotland too. The Rutledge purchase of land in 1757 and 1759 makes sense for a John, William, and Robert to show up there. I would guess then that Fannie came early 1770s, since Frances was born 1777 and brother John was older. Chronicles Vol II says that Fannie and William were married there in Ireland, key detail.
According to the Chronicles, wife Fanny and daughters Mary and Alice emigrated to New York City in 1812, and Fanny was widowed. William must have died that year or prior.
William is mentioned in the death record of his daughter Frances, in Trenton, New Jersey, USA, in 1856. No other details given, but it does point toward him which is helpful.