Actually, Major Alexander move back to Texas, and died there in 1927. From my research for the book "Texas Burial Sites of Civil War Notables":

Name: William J. D. Alexander
Civil War Service: Lt. Co. H, 8th Texas Cavalry. Major, TX Frontier Cav. Regt.
Born: Feb. 14, 1836, Maury Co., TN
Died: March 10, 1927, Center Point, Kerr County, TX
Occupation: Raised in Smith Co., TX. Physician in Denton and Erath Cos. prewar. Physician in Prairie and Lonoke Cos., AR postwar. Moved back to Texas c. 1912.
Education: U. of Nashville Medical College
Other: Brother Newton F. graduated from West Point
Buried: Center Point Cemetery
Grave location:
References: Terry’s Texas Rangers Website. Information from descendant Raymond Alexander.