I have reason to believe that Francis and Grace Jeacocks (pick your own spelling) lived in Stratford-upon-Avon, Warwickshire, England at the ened of the 1500's and in the early 1600's. Also in nearby Bishopton, and other places nearby. Four of their children seem to be Thomas, Francis, William and Catherine (called 'Catern", bpt. Bishopton 1613) came to America, possibly through Massachusetts ca. 1630-35, or possibly through Connecticut. Some are later found on Long Island, New York, especially around Hempstead and Jamaica. Catern m. Robert Ashman. Jeacockes moved from Long Island to Westchester Co., Dutchess Co., and possibly Ulster Co., NY in the early to mid 1700's. This is a vague recollection, but it might help.
Thomas A. Murray