As I explained in my previous post, I just don't see how the writings of Josephus can be used to justify belief that Jesus was crucified. The evidence provided by Tacitus is a little better. But good enough? I don't think so.
Writing in 116 Tacitus tells us that Nero blamed Christians for the burning of Rome. He explains that Christians follow "Christus" who "suffered the extreme penalty" under Pilate, and that the sect was in check for a moment, then broke out and became more popular.
If Tacitus' source for this information is reliable, then we have pretty good evidence that there was a founder of the Christian religion that was executed. But where did he get this information? Is he merely repeating what a Christian has told him, several decades after the supposed time of Christ? Or is he repeating information that he obtained from official Roman records, independently of simple converts? He doesn't say, so we're left in the dark.
One plausible answer is that he found out about Christians from his good friend Pliny the Younger. Pliny wrote a letter to the Emperor Trajan asking him how he should handle these people that call themselves Christians around 100 CE. He tells Trajan how he's going about dealing with them, and wants to be sure that he is acting appropriately. He tells Trajan that he asks them if they are Christians. He threatens them and tells them they need to worship the state gods. If they refuse, he has them executed, but if they relent he releases them. He says that he really didn't know what it was these Christians believed, so he brought in a couple and had them tortured so that they would tell him their beliefs. In this way he obtained information about Christianity.
Trajan replies to Pliny and tells him that he's acting appropriately. He says that he shouldn't bother seeking them out to punish them, but if they are brought before him and refuse to offer supplication to the state gods, they need to be punished. But if they recant, let them go free, even if they are known to be Christians.
Pliny the Younger is a very well connected guy, so if he is ignorant of what Christianity is in the year 100 CE you have to conclude that it is somewhat insignificant. He had to bring in Christians himself to find out. So what did these Christians tell him? The way mystery religions often operate is they tell outsiders the "outsider" story. Only initiates are given the secret, true information.
Did Pliny get true information, and convey that to Tacitus? Possibly. It's also possible he got information from gullible converts that received the information from second, third, and fourth hand sources. Or he may have received the "outsider" story from these adherents to the new Christian mystery religion. It's possible that Tacitus didn't even get this information from Pliny, but got it from a reliable source. Or he may have interrogated some Christians himself, and again got the outsider story. There's really just no way to know. And so unfortunately we just can't form confident conclusions about Jesus crucifixion from this type of data.
Habermas and Licona also appeal to Mara bar Serapion and Lucian. We're getting very late with these texts. I again don't see how firm conclusions can be drawn from these sources.