His life story is obscure, to the point that scholar Aharon Hyman wrote "Regarding the events of this tanna's life, much confusion has arisen, to the point that even if we say that [the lives of] two people are [recorded in his name], we will not solve all difficulties."
[2] The second Eleazar was son of the well-known Rabbi Zadok, and this Rabbi Eleazar provided the well-known testimonies from the house of Rabban Gamliel and was considered one of Rabban Gamliel's greatest students.
For example, R' Eleazar stated "Many times I entered after my father to the house of Rabban Gamliel, and they did not sweep the room of the beds on Yom Tov, but rather, they would sweep them on the eve of Yom Tov, and stretch sheets over them; the next day when guests arrived they would remove the sheets, and thus the house was swept on its own.
"[4] Similarly, R' Eleazar stated, Rabban Gamliel found a way to circumvent the prohibition on placing incense on coals on Yom Tov, by placing incense on coals in a closed container before Yom Tov, and opening the container on Yom Tov, causing the aroma to spread through the house.
[6] To resolve this discrepancy, Tosafot suggested that R' Eleazar's father was a priest and his mother a Benjaminite.