Josephus documents Rabban Shimon ben Gamliel I as an established figure in Jerusalem politics by 66 CE and rabbinic tradition names him among the last Sanhedrin leaders before the Temple's destruction, but neither source names his birthplace, his birth year, or a confirmed date of death; later tradition folds him into the legendary Ten Martyrs, a list usually set two generations later.
What would resolve this A datable document or inscription naming his birthplace or birth year, and an external account of his death independent of the later, chronologically strained Ten Martyrs tradition.
OpenRabbinics, Josephan studies, history of the Second Temple and SanhedrinFlavius Josephus, The Jewish War