WILCOX, William, of William and Priscilla, [born] June 24, 1733. WILCOX, William, of William and Priscilla, [born] Jan. 24, 1735.
Since June 1733 was before his parents were married, and 1735 was after he was baptized (and too close to Mary's birthdate), it seems likely he was born in 1734.