I would call an eye witness to the resurrection somebody who saw Jesus in his resurrection body in the 40 days between the resurrection and the ascension.
Right. So you agree, for instance, that Stephen the martyr and Paul were not eyewitnesses to the resurrection, despite having had a vision of Christ?
Even the women who arrived at the tomb did not actually witness the resurrection itself.
I assume we're going with the narrative presented in the gospels and epistles. In that case, I can't conclude this statement about the women, since the women could have been among the unnamed 500 "witnesses."
James the brother of Jesus was stoned for his leadership of the early Christians. Whether James saw Jesus in his resurrected form is not as important as the fact that James must have known that he was taking a serious risk to lead the early Christians but he did it anyway.
This couldn't be more wrong. The 9/11 hijackers knew that they were paying the ultimate price for their faith. However, they were not in a position to know for a fact that their beliefs were false. The disciples of Christ, as the argument goes, were in a position to know for a fact that Jesus either did or didn't rise from the dead. If he didn't, and they were making it up, why would they willfully die for their lie?
So seeing the resurrected Jesus is the entire crux of the argument, and you absolutely cannot say it is unimportant.
The only problem is that apologists absolutely fail at establishing the most important fact in the whole argument: that the disciples refused to recant their faith. Even the idea that the disciples were martyred is itself in doubt (aside from the cases of James and Peter), since the apologist's only sources for this are documents that he does not even regard as authoritative (scripture that was denied canonization, such as the Gospel of Andrew).
On top of this, no document in existence, regardless of its trustworthiness, establishes that the disciples were given the opportunity to recant and go free. This scenario appears to have occurred with Polycarp, but Polycarp was not an eyewitness to the resurrection.
The criteria for the "Why die for a lie?" argument simply have not been met.
Did James believe in Christianity or did he have some other reason?
James was obviously a Christian. I don't understand what you are asking me.
EDIT: Anybody who followed Jesus took a serious risk of being crucified for sedition.
Right... so... the best the apologist can do, as far as the "Why die for a lie?" argument is concerned, would go something like this:
1.) Suppose the disciples invented the resurrection
2.) After some time, the disciples saw that they were being targeted for martyrdom
3.) After several of them had been martyred, the rest would immediately stop preaching the gospel (since they know it is a lie)
4.) None of the disciples stopped preaching the gospel
5.) It is unreasonable to suppose 1.)
Of course, this does not stand up to scrutiny at all. If a Christian wants to take up this argument and defend it (either as-is or modified), then they can let me know and I'll be happy to expose the flaws.
They were obviously very committed to a cause, but what was that cause? I suspect that the early Christians believed something very different from modern Christians, so their commitment to that original belief does not support the modern belief.
Again, I'm not sure what your point is here.