It might be connected to the Second Jewish Revolt and constructed/used as a hideout for Jewish guerrillas fighting the legions of Titus and Vespasian. The fact that their is a legionary symbol their might suggest it was cleared out and one of the roman soldiers celebrated by carving his beloved legion’s name in the wall....
It was a Roman quarry and occupied by the Romans, although I suppose it was used by others later on.
People used old quarries to sleep in during the summer, even when they had houses because it’s 72 degrees down there, when it’s 102 on the surface. Old school air-conditioning.
Given the nature of the stone, the time, and location, I would be surprised if stone from this quarry was not used for the Second Temple.