Eliezer was active in the movement from 1941. He stayed at a hahshara in Budapest. Eliezer was enlisted in a forced labour unit and was an underground activist. In 1945 he became a member of the central leadership and engaged in rehabilitating the movement. Eliezer made aliya. He was a high official in the State Comptroller Office and at the Mizrahi Bank.
Eliezer resides in Jerusalem. His son, Avi, was killed IN 1982 in the First lebanon War.