Gay, this more than confirms that William Eugene Yeatman was a full time resident of Tennessee (after moving there from Texas, obviously), and never had anything to do with Australia. Unfortunately, the gentleman who indicated that Yeatman was buried in Australia, has actually convinced the cemetery personnel of the cemetery where a person of a similar name is buried, that it is the same person who served in the Tennessee regiment during the Civil War. Thank you very much for your help.
Apparently there is also an item at the Tennessee State Library which was written by William Eugene Yeatman, titled "Memories of the War of the State", and it may either be a book or an article in the Tennessee Historical Quarterly of 1953. If anyone knows of this, or has details of the publication, please let me know. I especially seek further biographical details of Yeatman. Thanks for all help and assistance in this important matter.