[1] His father, Joseph Thorpe Elliston, was a silversmith and planter who served as the fourth mayor of Nashville from 1814 to 1817.
[6] Elliston and his wife Elizabeth arranged to build a new mansion in 1859 to replace his father's plantation house.
[7] During the American Civil War of 1861–1865, the Union Army used the west wing of the Burlington mansion as a base, after it had occupied Nashville .
[2] After the war, Elliston was among several businessmen who called for the construction of a chapel in Lexington, Virginia, in honor of Stonewall Jackson.
[9] Elliston was a horsebreeder, and he entered his stallions in equestrian competitions such as the ones held by the Tennessee Agricultural and Mechanical Association, on whose board he served until 1870.
[10][11] His avocation was sport shooting; he was an officer in Nashville's Belle Meade Gun Club, and participated in many pigeon-shooting competitions.
The younger Elliston was active in competing in trap shooting, with tournaments being held at private sporting clubs.