Twelftree, Graham H. "Chatper Eleven: Jesus in Jewish Traditions." in Wenham, David (editor), The Jesus Tradition Outside the Gospels. Sheffield: JSOT Press, 1984, 289-341.
Twelftree in this paper is specifically investigating what Jewish authors tell us about the historic Jesus, not what they may have said which is less closely connected to this factual base of information (Wenham [editor] 1984, 289). He is particularly interested in what can be gleaned from Josephus and rabbinic materials.
Josephus lived approximately AD 37-92. He had strong commitments to his Jewish faith but also became fairly pro-Roman as he gained patronage from the imperial family (Wenham [editor] 1984, 290). Twelftree finds in his writings both a desire to pursue historical accuracy and a desire to mediate pece between the Jews and Romans so as to protect the Jews from harm (Wenham [editor] 1984, 292).
To consider what Josephus might know about Jesus and Christians, Twelftree evaluates passages where Josephus and the Gospels overlap. In the instance of the death of John the Baptist, he concludes that many of the same facts are recorded, but the accounts do not seem to use the same sources of information (Wenham [editor] 1984, 295).
If Josephus were interested in the events surrounding Jesus and Christianity, it is reasonable to expect he would have known them and could use them (Wenham [editor] 1984, 296). Twelftree does think it very likely that Josephus would have known a significant amount about Christians. However, he doesn't necessarily seem to consider Jesus as a very important character (Wenham [editor] 1984, 297). While Twelftree shows that Josephus makes numerous mentions of Jesus, he does not seem to consider his Messianic identity to be an important factor. A challenge in this regard is that some of our passages of Josephus come to us only as quoted by Eusebius, who may have interspersed Christian commentary with quoted text (Wenham [editor] 1984, 302). Twelftree evaluates numerous passages, each time considering whether it would be likely for strongly Christian statements to have been interpolated by Christian copyists. In the end, Twelftree concludes that the picture of Jesus in Josephus is almost always influenced by Christian copyists, with Ant. 18:63f as the only exception (Wenham [editor] 1984, 310).
Rabbinic traditions pose difficulties as well, often because they are hard to date, rather than due to editorial changes (Wenham [editor] 1984, 311). There is also a tendency toward historical revisionism, placing Jesus in radically different times or places than history would indicate (Wenham [editor] 1984, 314). Twelftree does identify some narratives about Jesus' trial and death, however, they don't seem to have much internal consistency and they suggest a lengthier process than can be found in the Gospels (Wenham [editor] 1984, 320-321). Twelftree concludes that the most reliable material suggests that Jesus had at least five disciples and that at least two of them may have had names similar to some of those mentioned in the Gospels (Wenham [editor] 1984, 324). This is exceedingly slim evidence.