Corporal Brockett was a member of Battery A, 57th Field Artillery Battalion, 7th Infantry Division. On 6 December 1950, as he was defending his position near Hagaru-ri, North Korea, his position was overrun and he was listed as Missing in Action. He was presumed dead on 31 December 1953. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

Brockett was awarded the Purple Heart, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.