There's no pension record for John W. Wilburn, and he's interred in the National Cemetery at Fort Smith, so he may have died during the war. All I know about him is his date of enlistment, and the remarks on his descriptive roll -- a farmer, age 36, born in Georgia, eyes black, hair light, complexion light, height 5'10".
There were a few other man named William Wilburn who served in Arkansas Confederate regiments, but they were all much younger than your William Wilburn -- late teens and early twenties.