when did Rabbi Shimon Bar Yochai die?

Yesterday we said in shiur, based on Rashi that R' Elazar's father Rabbi Shimon Bar Yochai had already died when they were young guys learning in front of Rashbag and Rav Yehoshua Ben Karcha. The Ben Yehoyada points out that this is difficult, since as we know, and we saw it today in shiur, he spent thirteen years in the cave learning with his father and the Ben Yehoyada insists that this story has to take place when R' Elazar was still young. Therefore he suggests that Rashbi was just not around but he was still alive