Charles,
It is highly doubtful that Joseph served. Very few men over 50 did, and many of those who enlisted at that age were subsequently discharged on account of age.
One more thing regarding William. Although the 1870 census shows William as 25, the 1880 census, where he is listed as W.J. James, shows his age as 30. If this is the correct number, he would have been only about 11 when the war started, and only about 15 when it ended. Without other proof of his age, this would be a logical explanation as to why we are having a hard time finding him in a Confederate unit.