I also have some Vermillion ancestors that lived in Guernsey County for a while.Maybe there is a connection, we also do not know any further back:
William Vermillion was born 29 Mar 1816 in Virginia. He died 17 Jan 1908 in Kenton, Hardin Co, Ohio and was buried in Kenton, Hardin Co, Ohio.William married Mary McClain on 3 Jul 1844 in Pickaway Co, Ohio. Mary was born 29 Jan 1820 in Bedford, Pennsylvania. She died Aug 1873.
1. William Henry Vermillion was born 1 Dec 1840 in Zanesville, Ohio. He died 9 Sep 1907 in LickingCounty, Ohio and was buried in Kirkersville, Licking, Ohio. William married Caroline Jane English on 26 Sep 1865. 2. John Oberland Vermillion was born 31 Oct 1845 in -, Ohio. He died 1 Nov 1921. 3. Charles Vermillion was born 6 Nov 1846 in -, Pickaway, Ohio. He died 1916 in -, Hardin County, Ohio and was buried in Smith Cem., Hardin, Ohio.Charles married Jane Fairchild. 4. Alford Vermillion was born 3 Apr 1848 in -, Guernsey, Ohio. He died 28 Dec 1852.Nancy Ann Vermillion was born 25 May 1849 in -, Guernsey, Ohio. She died 11 Jun 1853. 5. James Leonard Vermillion was born 5 Jan 1851 in -, Guernsey, Ohio. He died Sep 1937 and was buried in Kirkersville, Licking, Ohio.James married Jennetta Messick. 6. Mary Elizabeth Vermillion was born 13 Feb 1853 in -, Guernsey, Ohio. She died 31 1890 and was buried in Kirkersville, Licking, Ohio. 7. Lucinda Purdum Vermillion was born 11 Dec 1854 in Guernsey Co, Ohio. She died Dec 1942 in Hardin Co, Ohio and was buried in Preston Cem., Hardin Co, Ohio.Lucinda married Thomas Van Buren Wells, son of James Wells and Charlotte, on 11 Dec 1879 in Licking Co, Ohio. Thomas was born 5 Sep 1835 in Monongalia Co, Virginia. He died 16 Apr 1899 in Marion Twp, Hardin Co, Ohio.Civil War - 27 OVI Company C 8. Richard C. Vermillion was born 26 Jul 1856 in Ohio. He died 31 Mar 1859 in Ohio. 9. Oliver Hess Vermillion was born 6 Mar 1857 in Ohio. He died 21 Dec 1947 and was buried in Porter Twp, Delaware, OhioOliver married Mary Browning on 14 Oct 1883. 10. Sarah Hannah Vermillion was born 20 Jan 1860 in Ohio. She died 19 Jun 1952 and was buried in Kirkersville, Licking County, Ohio. 11. George Vermillion was born 22 Apr 1861 in Ohio. He died 28 May 1861 in Ohio.