This William Barneycastle appears to be William Thomas Barneycastle, according to a post on GenForum from Winifred Brunson, a known researcher of the Barneycastle line. Her post of June 16, 2002, states the following:
"...while none of the Civil War records I've obtained bear an age or birthdate, I believe William Bay [Barneycastle], who would have been abt 52 at the time, enlisted in the Conf Army as a Private..his son, William Henry [Barneycastle] wld have been abt 11 at the beginning of the War. William Barnacastle enlisted on Nov 1, 1862 at Camp Tattnall, FLA for a period of 3 years. He was paid $24.40 for the use of his horse and enlisted as a Substitute for R. H. Johnson Confederate 3 Battn Calvary, Co B.(Florida)...].