Reubin Thornton appears as a lieutenant in the 2nd Georgia State Line, no company listed. Records for this regiment are scarce since it was raised under authority of the State of Georgia, not the Confederate government. That explains why we don't easily find H Z Day in Confederate military records. Unfortunately the Georgia State Archives is by far the best place to look for records of State Troops.

Here's a book on these unusual soldiers --
http://books.google.com/books/about/Joe_Brown_s_Pets.html?id=VY9iw4GzIGwC