Any Historical Sources That Dispute The Existence Of Jesus?

[DeistPaladin]

You interpret these passages as if they were written to Docetists in order to persuade them to believe that Jesus "came in the flesh". But rather the context makes clear that John is giving instructions to those who already believe this

Well aware but that doesn't take away the strangeness of admonishing believers to think that Jesus was a flesh-and-blood being on the basis of faith. If this is the same "John" who was supposedly a disciple of Jesus, I might expect him to caution believers not to be persuaded by these Docetics on the basis of what he had seen and recent history. I would expect him to denounce the Docetics as crazy, not as blasphemers.

A non-existent Jesus can't appear to anyone.

But it does fit with an alternate scenario, where Jesus got his start as a Celestial King (ala Revelation, the first book of the NT), came down to earth in some vague time and place (ala Paul's epistles), the story was fleshed out in parables (possibly Mark's intent) and the parables were later thought to be true stories.

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The evidence for Jesus is obvious: four biographies of his life,

Play the theme to Galaxy Quest. Someone just referred to the Gospels as biographies. Seriously, dude, they're mythology, not historical documents. Even taking the Christian claims about the authorship of each Book at face value, these are not eye-witness accounts.

Mark: Companion of Paul. Not an eye-witness.
Matthew: A discredited account, seeing as how he lies his ass off about supposed OT prophecies.
Luke: Not an eye-witness and even says so in his intro.
John: The advanced theology indicates a very late date of authorship.

All four accounts contradict each other so badly there's no way to put Jesus' life into a coherent timeline.

references in Acts

A fanciful book containing all manner of miracles and magic. Do you believe that those of the faith can speak foreign languages, cast out demons and heal the sick? If yes, you're nuts. If no, how do you take the accounts in Acts seriously?

and the New Testament epistles

...which offer vague references to a Jesus at best. Paul flatly denies that Jesus had lived within his lifetime (1Cor 15:8). Additionally, the epistles are dubious sources. Half of Paul's epistles are of questionable authorship. Pseudo-epigraphy and interpolation were common problems for religious scripture of the time.

and other references in both Christian and non-Christian sources (most notably Josephus and Tacitus, two excellent and reliable historians).

Josephus: TF is a glaring forgery. Jamesian references names "Jesus Bar Damneus".
Tacitus: Late (2nd century), oblique (doesn't mention Jesus by name), odd reference to Pilate as "procurator" (term used in later years of Rome's empire), and 2nd hand (relating what he was told about or by the Christians).