Well, way I see it -- and please point out if this premise is wrong -- it's sorta like this: if I were to go into my super-villain lair and hop into my time machine, armed with the stories about a guy, would I have a reasonable chance to tell that it's this guy and not that other guy? Or even narrow it down to a group of similar guys?
Because ultimately that's what defines someone. And conversely, if the story doesn't need enough information to define a person, then why does it actually need a historical person?
I mean, let's try that exercise for Socrates. We know roughly where he lived, we know what he teached, we know the kind of opinions he had, we know at least two direct disciples of him, etc. I'm pretty confident that if the stories are anywhere nearly reliable, you could find a guy meeting a reasonable number of those pieces of information.
Or Caesar. Well, that one would even be easy to find. We even know what he looked like, plus, you know, if all else fails, look for a guy leading an army in Belgium.
Alexander Macedon... same deal.
Now let's try the same for Jesus:
- do we even know in what year to go to see the crucifixion? I mean, come on, I must dial something into this time machine

Nope. Even early Church fathers, not some obscure gnostics, are all over the place with it, and mostly base it on numerology and making it fulfill some prophecy. And even from the 4 canonical gospel, one doesn't point at the same year as the other three.
- on what date? We don't know, and the early Christians don't know either. What got use 25 March -- and from there a conception on 25 March too, which got us a birthdate on 25 December -- are simply considerations that someone liked it to be on the spring equinox, the same date as they thought God created the Earth. So again it's something that is just pulled out of the ass, not something they knew. (And in turn that leaves us with even less to nail the year.)
- ok, let's say we want to witness the nativity first hand then? In what year? Not only Luke differs from Matthew by 10 years, but at least one church father makes Jesus be born circa 70 BC. But really, if you read their texts, they don't know. It's the same hare-brained numerology and making it fulfill some prophecy, rather than "sure, we have these guys who knew him."
- in what city should we look for it? It may seem easy. Bethlehem, right? Actually, even that isn't clear, because it's there just to fulfill a prophecy. There are a couple of biblical scholars from prestigious universities and all, who think Jesus was most likely born in Nazareth and the Bethlehem bit was added later. (Also note that the earliest gospel, Mark, doesn't make any note of where he was born. It's a detail added some almost a century after the event.) Bummer.
- but ok, he travelled later all over the place, so maybe we can intercept him in one of those towns? Actually that comes from Mark, who most likely just made it all up. We know that because even early Church fathers like Origen tried to make sense of it, and gave up. Origen concludes that the journey must be taken as symbolic rather than literal, when it becomes clear that it makes no sense at all. Mark is that thoroughly unfamiliar with the geography of the place, that for example he has Jesus go south at one point and manage to pass through a city some tens of miles north of where he started.
- exactly what did this guy do or preach? It may seem easy, but after you remove stuff that had to be made up -- miracles, stuff that symbolically fulfills some prophecy, public speeches, smart Aleck answers which clearly wouldn't have worked that way in a theocracy, impossible stuff like single-handedly clearing all the tens of acres of the temple of the merchants, stuff that involves physically impossible stuff like the two storms on the Sea of Galilee, etc -- we're not really left with much. In fact, we're left with almost nothing.
But there's an even more damning aspect: remember Mark's unfamiliarity with the place? It goes deeper. Mark is thoroughly unfamiliar with the language, customs, etc. A large motivation for Matthew to write his own version of Mark seems to be to just correct the many mistakes in Mark.
But that is damning by itself, because Matthew -- and for that matter Luke -- really just copies most events from Mark and corrects it to something more believable. If Matthew or Luke were knowing anything about Jesus and his ministry and deeds, why would they need to copy from Mark, who obviously isn't a witness? So really we're stuck with some events that are corrected by Matthew and Luke to something more believable, but nevertheless originate as tall and wrong tales from a guy who doesn't know what he's talking about.
So really, we can also throw away just about everything that originated in Mark. As I was saying, we don't have much left.
- well, ok, but we're still looking for a rabbi, right? Actually, we don't even know that. There is a good case to be made that someone who (A) did manage such an attack on the temple, and (B) was crucified for it, could just as well be a bandit. Plus, there's the detail of that Jesus Barabbas who could really be a duplicate character, the bad Jesus.
Plus, even the canonic gospels occasionally have WTH moments. E.g., in the 3 synoptics, Jesus just loses it in the temple and kicks everyone out. Not in John. In John he first makes a scourge out of leather strips (incidentally, yes, it's the same Greek word as for the scourge used on him before the crucifixion), something which involves time and premeditation, then goes with it and drives the people out of the temple. That's not exactly peacenic Jesus, you know?
- but ok, we're still looking for a miracle worker, right? I mean, laying hands on people, and commanding demons to go away, and whatnot? Again, not necessarily.
One of the non-canon gospels offers a horrifying description of HOW Jesus drove the demons out of a girl: he tied a cloth around the girl's head and eyes and set it on fire. And of course, the fire only hurts the demon, not the girl, see? Incidentally that's to this day the justification for cruel exorcisms, and often crippling or killing people in the process. When idiots in Africa put caustic stuff in kids eyes (usually leaving them blind for life) or whatnot, the same justification is given: see, it is to hurt the DEMON and drive it away.
So really, we might have to look for some deranged lunatic performing that kind of cruel stuff. Which might actually explain why the progressive Pharisees accuse him of working for Satan when he does those exorcisms.
- even if we nailed the year, and were to look for some crucified guys at passover, where would we look? On a hill, right?
Well, actually that's another piece of symbolic stuff. Actually the Romans crucified people (or placed heads on spikes, or whatever) in low places. A human effigy on a cross placed high was a "tropaeum". Really, the same thing that is the root of the word "trophy". It was done for funerals, or as a display of victory, etc. Sometimes actually placed on top of a hill or monument, e.g., see the one at the Tropaeum Traiani. And especially emperors did that all the time.
Plus, it was standard for hero stories to have them die in high places. Again, it's a matter of symbolism. Criminals were executed in low places, while heroes died on a hill.
So we actually see the gospel writers, pull a symbolic sleight of hand that is not obvious to modern people, but would not be lost on audiences from their time. The dishonourable crucifixion is turned into Jesus being a tropaeum, a symbol of victory, for God. It's a continuation of that allegorical dressing him in purple and all.
So, anyway, a more reasonable expectation would be to look somewhere lower, and possibly a tree rather than a cross.
That is, if it even was a crucifixion at all. We know that in at least one place in Paul, namely in Philippians 2:8, the "even death on a cross" is actually a later addition. We know that because that verse is in a poem in Greek, and the added part breaks the meter. At any rate, we have one instance where someone felt they had to insert that into Paul's epistle. How many other such forgeries are there? Hard to tell, because the very few other places where he mentions a stauros (actually a pole, rather than a cross, but then the patibulum would be carried by the condemned anyway) aren't in poetry.
- how old was he when he was crucified? I mean, maybe we can use that to identify him. We don't know, and the early church fathers had no frikken clue either. We know from Irenaeus for example that those who want a ministry starting at 30 years old, and taking 12 months from there, actually only base it on hare-brained numerology and symbolism. Irenaeus himself thinks Jesus preached well into his fifties. Other favour his dying at 40, because 40 is such an important number for God. What we see is that they don't know. They're just making up something that would be awesome if it were true, not knowing it.
- but he was at least called Jesus, right? Nope, we don't really know that either.
Paul for example in the same poem in Philippians 2 seems to say that Jesus was given that name by God after he died. And it's not even preposterous once you realize that a bunch of people at the time expected a messiah that is basically a second coming of Joshua, i.e., Jesus. The two are actually the exact same name. So really it could be a guy that was called anything whatsoever, and who gets the name Jesus by becoming the messiah.
Etc.
Basically if we had a time machine, we actually have a big case of "bugger me if I know". We don't have much to go by to find this Jesus guy, because practically all details are made up.
Which in turn gets me to ask: so did they need a historical Jesus? If they made up just about everything they needed about him anyway, did they need to start from a real person at all? And even if they did, a person which probably was nothing like the guy in the NT, didn't do the same things, didn't go to the same places, etc, can one still call him the "historical Jesus"?