Josephus? His "Testimonium Flavianum" is doubtful at best. Richard Carrier presents a good skeptical case against it: [richardcarrier.info] and other articles. The case: it is out of character for Josephus, not only in the way it presents JC, but also in vocabulary and style. To get a hint of how Josephus would like have viewed JC, consider his discussion of self-styled prophets Theudas and "the Egyptian". He comes across as very skeptical about those two. Also consider that he described a riot in the Jerusalem Temple that was provoked by a Roman soldier exposing himself. The Roman garrison commander sent in some troops with clubs to suppress it. Why that and not JC's Temple temper tantrum? His driving the merchants and the moneychangers out of the Jerusalem Temple.

As to the Buddha, is there any documentation of him that is close to when he lived? Especially documentation by people who are not his followers.

Plenty of miracles were attributed to him. Like his dreaming that an elephant entered her side, and when he was born, him walking and then announcing that he is on his last reincarnation. [en.wikipedia.org] [pbs.org] [padmasambhava.org] [einterface.net]

Miracles aside, the four passing sights - an old man, a sick man, a dead man, and an ascetic - seems a bit too schematic. So I think that there is good reason to be skeptical of his canonical biography.

Seems like a variant of my part-history, part-myth option.

@lpetrich Perhaps, but you didn’t give that option for the gospels and Jesus ?

Like the walking talking cross in the Gospel of Peter and Jesus Christ as a little boy in the Infancy Gospel of Thomas.

The Magdalene was not a hooker that was a rumour started by the early popes to discredit her and there is far more historical evidence for her (as a disciple of John the baptist, who definitely did exist) than for the carpenter of Nazareth.
If you have read the Gnostic Gospels you should know this.