In 1867 my folks fled West for Texas but got way laid in Magazine, Logan County, Arkansas. My father was born in Boonville just West of Magazine.
There are some six Joseph Youngs in Tennessee units. I'll see what I can find of these fellows.
However, I should think you start with the Arkansas Confederate pension applications as well as the Arkansas census for 1860, 70, etc. Here you might find out where he was born which will narrow the search considerably.
George Martin