In those days, there was fighting and dissension in Judea between the Pharisees and the 'brigands of our people' who followed the son of Joseph, etc ...[lacuna] Eleazar, who committed great crimes in Israel until the Pharisees overcame him."
This appears to confirm what the Pagan Hierocles wrote, as told by the later Lactantius, against Jesus:
“affirmed that Christ Himself was put to flight by the Jews, and having collected a band of nine hundred men, committed robberies”
(Lactantius, Divine Institutes, 5,3)
The mention of Eleazar in the Josippon, precisely in the same point where a rebel "son of Joseph" is mentioned, makes it clear that the "son of Joseph" who is meant is precisely the Jesus also meant by Hierocles, i.e. a Jesus active during the First Jewish Revolt (66-70 CE): Jesus son of Saphat.