Rabbinic sources record his teaching, his hiding from Rome, and his tomb at Meron, but no source gives an actual birth or death year, and the later literary Shimon bar Yochai of the Zohar complicates any single dating further.
What would resolve this A datable inscription or external documentary record naming a birth or death year for the historical tanna, independent of the devotional yahrzeit tradition and of the Zohar's own literary framing.
OpenRabbinics, history of the Mishnaic and Talmudic periodGershom Scholem, Major Trends in Jewish Mysticism