I looked at your family tree on Ancestry and see that you also have this man known as Sharp. In fact several records show his name as Thomas S (presumably Stewart) Sharp. People who are trying to help you looking for a James Thomas Stewart will be spinning their wheels.
I checked court records and recorder for Pima Co. AZ (online for free), but there are two many men by these various names to home in on the right one.
However, I certainly would suggest trying to get an obit or funeral record from Tucson, or from KY which is where you live.
I also note that a Ronald Stewart Sharp (son of Thomas S. Sharp and Dorothy Marie Reece) was born and died in Barren Co., KY in 1951.
He is buried here:http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=sh...
Mistakenly indexed as Donald.
If this is the right Thomas S. Sharp, then he and Dorothy apparently had several other children listed in the KY birth index.
Is this the right man? or not?