The only argument that ever really swayed me with the whole historical Jesus thing was something I read a while back by Christopher Hitchens (I think he's the one who wrote it. Maybe it was Ehrman, I don't remember). It said that there were things written in the bible about Jesus that your normal, average person looking out for the messiah would not have expected of the messiah they thought was coming. For example, the Jews believed Jesus was going to be a great leader, and the guy they portrayed in the bible was just some poor shmuck. Why wouldn't they have made him a great leader if they were just making it all up? One reason might be because a real guy existed that was dirt poor. Stuff like that lead them to think it couldn't ALL be made up. Another one had to do with his birthplace. Same sort of thing where they thought the messiah was going to come from one place, and the 'real' Jesus didn't come from there, so they had to create that census bullshit to get Jesus to be 'from' where he was supposed to be from.
Again, I know of zero empirical evidence.
This definitely sounds like Bart Ehrman. Unfortunately this is nothing more than an argument from personality incredulity. "I don't see why anyone would make it up, therefore it must be historical". The biggest problem with his argument is that he treats Jews as one monolithic group with no diversity whatsoever. There were dozens of Jewish sects at the time, many of which we don't know what they believed. His argument about what they would or would not have believed is completely unsupportable. Furthermore, he assumes that a crucified messiah means a failed messiah; even the Christians believed in a conquering messiah, except he had to sacrifice himself first to pardon sins before returning within their generation to kick some ass.
Empirical evidence isn't really relevant here since historical methodology is fundamentally different than that of science in that it's about trying to interpret the past using the bits that remain. You'd be hard-pressed to find any empirical evidence of any ancient person who pretty much wasn't a king as to have coins and statues made of them. What is relevant here is that the only sources we have to work with in order to interpret the history of Jesus are theological in nature. It's not atypical for people of great prestige to have had myths surrounding them such as Alexander the Great being born of a virgin, but the problem is that the historical Jesus we are discussing is nowhere to be seen in the sources. Instead, it's only Jesus Christ, the son of God who performed miracles, died, resurrected, and ascended into heaven. There's not even any external corroboration, which is key when assessing history based on text. Any "real" Jesus is only assessed only in terms of what parts of the sources could
be based on real history, but there is no legitimate historical discipline that just plucks historical facts from a theological narrative. At least with Socrates we have some sort of identity which can be attributed to him (even if just as in the same way as with Paul Bunyan and Robin Hood) whereas most of the scholars who argue for historical Jesus essentially argue for a complete non-entity who we can know nothing about.
That's my take on it, anyway. I'm not particularly well-read on the subject, but this is my understanding of the nature of the texts and historical methodology.