Habermas and Licona believe that Jesus' brother James had been a skeptic prior to the resurrection and subsequently converted to Christianity. They are not claiming that this one fact alone proves that the resurrection occurred, but that this one event, taken with others that are agreed upon by the vast majority of scholarship, does point to the resurrection as an actual historical event. This is part of what I described as their minimal facts approach.
Do we really know that there was a man named James, brother of Jesus, that had been a skeptic prior to the resurrection and subsequently converted? I've shown that the evidence offered by Habermas and Licona simply do not warrant this conclusion.
Habermas and Licona point to the fact that two extra biblical sources mention the martyrdom of James. They first appealed to Josephus and then to Hegesippus. I discussed Josephus last time. Hegesippus' comments on James death can be viewed here.
It's interesting to compare the account of James' death from Josephus to that of Hegesippus. What's obvious immediately is that the circumstances are entirely different. This should be an immediate clue to the reader about the conclusions that can be drawn. Since the circumstances that lead to his death are different we should probably start by being agnostic about the reasons for the death.
But this is not how the apologist operates. James must have died on account of his Christian faith. According to Habermas and Licona, James apparently held this faith with conviction, to the point where he was willing to die for it. Josephus says no such thing, but Hegesippus does. Should we prefer Hegesippus to Josephus? Why? No argument is made.
It's reasonable to conclude that James was an important leader of a Jewish sect that operated around the time of the life of Jesus. It's reasonable to conclude that he was killed. We know that some sources imply that James is a skeptic, others say he's the leader of Jerusalem Christians. One source says he was killed due to the machinations related to who would become high priest. Another source says he was killed for professing Christianity. Does this entitle use to just assume that in fact he was a skeptic prior to the resurrection, became a Christian based on what he perceived to be a personal appearance from Jesus, and died as a martyr for this belief? Absolutely not.