Before you give up on W. H. Parker from Carroll Co AR, please be advised that the Parkers and Gaithers moved pretty much together from NC to TN to AR. The listing of Gaither Cemetery at: http://www.rootsweb.com/~arboone/gaither.html lists a "W. H. - 23 May 1829 - 14 Nov. 1908" on line 103 under Parker.
I believe those dates may be relevant.

James Troy Massey's book "Confederates Buried in Boone, Baxter, Carroll, Newton and Searcy Counties, Arkansas" on page 20, under Gaither Cemetery, lists as follows:
"PARKER, W. H., Private, Co. F, 1 Arkansas Mounted Rifles or Co. E, 38 Arkansas Infantry.". The Adairs, Coffman and Wasson listed with him are all my relatives as was the Gaither for which the Cemetery was named.