Boy, is this poor fellow the victim of mistranscription. He is on the 1900 census as "David Houston" because his first name couldn't be read and on the 1910 census as "Dewitt Hariston" because his surname couldn't be read. In both years he was a farmer in Bowling Green, Caroline County, VA. On the 1910 census he is
not listed as a veteran. I don't know about recruiting guidelines in Virginia; I thought that they were drafting just about everybody.
@lupaglupa certainly may be right: there may have been some sort of physical issue.
https://www.lva.virginia.gov/public/guides/opac/conpenabout.htm#Links says that it has a database of Virginia Civil War pensions but either I took a stupid pill this morning or it isn't accessible via Internet
Obviously, if he didn't serve there won't be a pension--but the Census isn't always accurate and I thought that I'd check this back up.