Tacitus is problematic too, but even accepting it as authentic, most scholars do not rest any case for the historicity of Jesus on it because Tacitus wrote in the 2nd Century and was probably only repeating what Christians in Rome were saying. He gets Pilate's title anachronistically wrong and doesn't know Jesus' name (he only calls him "Christus," a title, not a name and not a title that wouldhave appeared in any Roman record).

The Pilate stone is not especially probative since Pilate was abundantly attested by Josephus as well as Philo and no one ever really doubted that Pilate existed.

The historicity of Jesus tends to be defended more by the the James Passage of Antiquities, the letters of Paul (particularly two mentions of Jesus having brothers), by evolving Christological patterns in the Gospels and arguments from dissimilarity such as the crucifixion itself (the argument being that there was never any expectation in Judaism that the Messiah would be killed, so it seems improbable that a Messianic sect would make up a dead Messiah)..

If we accept that Jesus was executed under Pontius Pilate and baptised by John the Baptist, does that also mean that history supports his divinity to some extent?

Of course not. Augustus Caesar was deified after his death. We have tons of evidence for Augustus Caesar. Does that make his divinity more likely?

If it vindicates the Gospels as historical documents

It doesn't, though. For numerous reasons, the Gospels are considered to be historically unreliable and sometimes demonstrably fictionalized.The presence of a few real names is a common feature if fiction (think Forrest Gump).

Preface

The Short answer is no: Tacitus is not the only or main reason why modern historians (whether Atheist, Agnostic, or Christian) believe the historical Jesus existed. I am going to copy and paste my answer from a previous post and also suggest that if you want in depth answers into what evidence we have for the Historical Jesus to read one of these two books:

• Ehrman, Bart: Did Jesus Exist?: The Historical Argument for Jesus of Nazareth
• Crossan, John Dominic: The Historical Jesus: The Life of a Mediterranean Jewish Peasant Ehrman is a very vocal Agnostic (borderline Atheist) and Crossan is a Christian, just to give you both sides of the coin. I recommend Ehrman because he's one of the most engaging historians on this topic, period.

Why do historians overwhelmingly agree that Jesus was historically a real person?

First, we need to address one key issue that most people don't understand, so people on both sides of this argument like to take certain things out of context. It needs to be known that we have practically no primary sources for many secondary (non-monarchs or major political figures) characters in antiquity. This is what the historical Jesus was (a secondary character in his day). If we simply say "we have no archeological evidence, so he doesn't exist" then we need to say that Aristotle and Socrates did not exist because, like Jesus' story, we are left with written accounts that have been repeatedly copied through various generations.

Now when it comes to the historical Jesus (and what we know of him) well it's simple in a few ways. The first, is that although the gospels and other New Testament books were all written decades after Jesus died (however Paul started writing between 45-49 BCE), they are independently attested. Yes, from a historical perspective (and personally for myself since I am agnostic) the miracles and resurrection are considered embellishments to help encourage early people convert to this new Jewish sect.

What does this mean

Now although much of this information cannot be relied upon for historical purposes, some of it can pass the test of historical plausibility. What do I mean by that? Well, every historian, when examining evidence, has a set of criteria they must use when comparing written accounts of any event. Part of doing this, is taking these four accounts, and cross examining with each other and seeing if any of the minor details (things that lack religious implications that would be less likely for people to make up) correspond to most or all of the documents. What you'll find is that many of these minor details correspond consistently in ways that you wouldn't expect-- this is something you almost never see with mythical figures.

You'll also see that the early Gospel writers likely had to create explanations for certain things about Jesus because his name was likely somewhat known around the time of his death. I'll give a brief example:

Two of the gospels deal with the birth of Jesus. Without going into too much detail, it's easy to make the argument that both Matthew and Luke did not get their information for this narrative from the same source. They are constantly at odds with each other over many specific areas of this story (example: in Matthew, Mary and Joseph already lived in bethlehem and then had to move to Egypt and then, years later, move to Nazareth. In Luke, Mary and Joseph lived in Nazareth, traveled to Bethlehem for a theoretical tax registration, waited there for 32 days after Jesus was born, and then returned immediately to Nazareth).

Most historians believe it is likely that both of them made up nearly all (if not all) of these stories parts to their stories because they were trying to fulfill the prophecies from the Old Testament. See, in the book of Micah, it was predicted that a savior would be born in the city of David (Bethlehem), so these writers wanted to make sure that Jesus fulfilled this prophecy. But wait, they had a real issue to deal with. It was probably well-known that Jesus was from some small town called Nazareth, thus he didn't fulfill that part of the prophecy. So, to deal with this, early gospel writers created these narratives to explain how this person from Nazareth could have still been from the city of David.

If Jesus was a mythological figure that sprung up out of thin air, there would be no reason to say he was from Nazareth, they would have said he was from Bethlehem and just left it at that. This is what we typically see for made up figures. Keep in mind that this is one of dozens of examples where the writers did this to meet personal agendas of their time.

What historians also find is that it is nearly impossible for a sect or cult to immediately spring up without a founding figure. After Jesus' death, the remaining followers were probably a group of people of about 20-30 people, and it expanded rather quickly -- probably hitting the hundreds within the decade after his death and by 50 CE, they had spread throughout the Roman Empire. Most scholars believe that the book of Mark, written between 65-70 BCE, was actually written in the city of Rome for a local church there. This type of growth and expansion is, by historical standards, incredibly fast. The rapid rate of growth suggests, for historians, that a real figure of Jesus existed, had a few followers who immediately disbanded after his death. Yet, for those whom remained, they started preaching about his life and resurrection, which was likely very enticing for their day.

I hope this gave you a glimpse into the answer for this. If you'd like more examples I can provide them.

Edit: to correct a wrong link

I would like to say there is ANOTHER problem with Tacitus; the Christians of his own time seem to unaware of Nero choosing to blame them for the Great Fire.

The apocryphal Acts of Paul (c. 160 CE) has Nero burning Christians to death around the death of Paul (i.e., 67 CE) because Nero has seen some guy named Patroclus who had supposedly died and was told that Christ Jesus would "overthrow all kingdoms" and this man was now a solder in Jesus' army (so the Christians themselves have Nero reacting to a possible attempt at overthrowing his government)

On the other hand, "The Acts of Peter" (late 2nd century CE) claims Nero considered to "destroy all those brethren who had been made disciples by Peter" but had a dream after Peter's death (either 64 or 67 CE) which said 'you cannot now persecute or destroy the servants of Christ.' and a frightened Nero 'kept away from the disciples . . . and thereafter the brethren kept together with one accord . . .'.

Moreover, Josephus and Pliny the Elder who were both in Rome in 64 CE don't mention Christians at all which would be highly unlikely if Nero was trying to blame them for the fire.

So not only do non-Christians who were in Rome at the time not notice Nero's persecution of Christians for the burning of Rome, but the Christians themselves appear to be unaware of it as well and instead give two wildly contradictory accounts — either Nero killed Christians with Paul some three years after the fire because he was told this cult would "overthrow all kingdoms" by one of their members, or he had a dream resulting in him leaving them alone which could have been as early as 64...the year of the fire. The passage is therefore highly suspect and adds virtually no evidence even for early Christianity. In fact, Richard Carrier in "The Prospect of a Christian Interpolation in Tacitus, Annals 15.44" Vigiliae Christianae, Volume 68, Issue 3, pages 264 – 283 (an earlier and more detailed version appears in Hitler Homer Bible Christ) shows strong evidence that the "Their founder, one Chrstus had been put to death by the procurator, Pontius Pilate in the reign of Tiberius." phrase is an interpolation.

What "rate of confidence" would you say historians have for Jesus being historical? Is it more like 60 or 70 percent, or is it close to 100 percent?