Is there any Jewish evidence for the historical Jesus? The best evidence we have is from Josephus. In this video, the Apologetics Guy talks to us about Josephus says.
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A Christian Response by Stephen J. Bedard
Personally, while I view Jesus as a historical figure, I think all the extrabiblical evidence is pretty much useless in establishing his historicity directly. I tend to agree with scholars like Olson and Allen that the Josephan references are likely forgeries. The Tacitean reference I see as likely a result of knowing Christianity already (same as the Talmud, Suetonius, and others), following Prchlík and Schaefer. I think, honestly, Paul is all we really have for the historicity of Jesus, but I think he overwhelmingly supports Jesus’ historicity at that.
What I think they are most affective for, in regard to mythicism, is establishing that there were no early Christian mythicists anywhere. Basically, once you disregard the mythicist misconstruing of Trypho, you can ironically form an argument from silence against mythicists, in fact (something way more effective, imo).
I also think that if one looks at the arguments from silence against Jesus through Marxist theory, then the mythicist positions fall apart on logical and ethical grounds almost entirely. It really saves a lot of time and energy in defending his historicity if one goes the Marxist route, without having to deal with the bogged down mess of trying to strenuously argue that X passage is authentic, and then go one step further and be like X is also independent and all.