Here is my best evidence for this William Gillihan. I have lots more, but this covers the period around the time of the Franklin petition.
The Gillihans and the Walkers were part of the Scots-Irish settlements of Old Augusta Virginia, later called Botetourt, then Wythe and Washington counties. The Walkers were there by the 1750s. We know that William Walker moved to the Laurel Fork of the Holston River in 1778 or 1779, and we first find record of John Gillihan in nearby Sullivan County in 1778. So perhaps they migrated together, as clusters of families often did. William and Clement Gillihan, probably the brothers of John Gillihan, in 1778 and 1779 when the Walkers and John Gillihan were moving into the Holston area, were in military service (see below). Clement befriended Mark Hardin during the war, followed him to Kentucky, and married his daughter, Nancy Ann. William went to East Tennessee, near John, where he married Nancy Walker few years before her father’s death. Nancy inherited some of her father’s land in Washington County, Virginia. After giving birth to two children (Thomas and Elizabeth), Nancy died sometime between 1784 and 1787. In 1787, William remarried to Frances Tadlock in Greene County, Tennessee, just west of Sullivan. This area was then part of the State of Franklin. That same year, William signed a petition in the State of Franklin, an ill-fated attempt to form a separate state in East Tennessee from 1784 to 1788. Interestingly, Davy Crockett was born in Greene County (then State of Franklin) in 1786, in a cabin on the Nolichucky River.
William Gillihan, our first proven ancestor, was born about 1750, probably in the Scots-Irish settlements of western Virginia or in Pennsylvania if we can connect him with the Gillighans there. William served in the Revolutionary War, enlisting in Virginia and serving from 1775 to 1781. His brother Clement (or Clemmans, Clemmons, Clemence, various spellings) enlisted at Cheat River, Monongalia County, Virginia (now West Virginia) in January of 1777, serving as a private in Captain David Steel’s company and then under Captain Benjamin Biggs’ Company of Colonel John Gibson’s 7th Virginia Regiment until the end of the revolution. While in the war, Clement became friends with Mark Hardin; the two went to Kentucky after the war and Clement married Hardin’s daughter, Nancy, in Nelson County, Kentucky on August 26, 1790. Clement settled in Washington County, Kentucky.