Thomas was born on March 3, 1939, to Dewey Bryant Custer and Alice Faye Parker Custer.  He was born in Laredo, and his childhood was spent in Bruni, Texas.  He graduated from Beeville High School and began working at a bank shortly after graduation. Tommy was a proud graduate of the Southwest Graduate School of Banking at Southern Methodist University.

Tommy was a banker for over 50 years and loved every minute of his long career.  He also enjoyed his leisure time boating, fishing, flying, hunting and golfing.  He was a longtime member of Lochinvar and Augusta Pines golf clubs.

Tommy married Christine Hensley in 1964.  They had one daughter, Deanna Kay, in November 1967.

In 1980, Tommy and Pamela Pittman were married.

Tommy is survived by wife Pamela, daughter Deanna Kay Custer, stepson Lain Custer, granddaughters Madison Claire Custer and Haley Austin Custer Rouse and her husband Tyler James Rouse, and great grandson TJ Rouse.