According to the Shita that he was in the time of Moshe, he wasn’t Jewish, either. Chazal say that when Kalev said Sar Tzilam, that their protection is gone, that is referring to the fact that Iyov died. He lived in Eretz Kena’an and his Z’chus protected them.
Also, if he was from the three servants of Paroah, he wasn’t Jewish, either. That could be the same one who Kalev was referring to.
I once heard a cute thought regarding the Shita that he did’t exist. This is the worst Tzara for him. Imagine, after having gone through all that he did, to be told that he didn’t even exist. We can relate to that when we hear of holocaust deniers and the great pain it causes in those who went through it.