The video shows the guard who was on duty that night going after the proscribed routine in a sloppy and unattentive manner.
The Gilboa prison break has seen intense public and governmental scrutiny leveled against Israel's prison services.
Gilboa Prison's former commander and the former intelligence officer had allegedly known that female prison guards had been sexually assaulted.
Among the captured is Muhammad Zubeidi, who was arrested in Jenin and is the son of Gilboa prison escapee Zakaria Zubeidi.
Ben-Gvir's decision comes against the background of several serious incidents of injuries to soldiers in the Israeli prison system and the Gilboa pimping affair.