Jasper I think was only 17 when he turned. He says that he was almost seventeen when he joined and that his military career was short lived. It doesn't actually say how long he was a soldier but I can't imagine it was too long like maybe a year. which would make him 17...maybe 18.
Actually, Eclipse says he was almost 17 when he joined the Army, in 1861. However, the Battle of Galveston took place in 1863. so he was atleast 19, if not having turned 20 before his being turned. : )