Jewish Jesus and the Third Quest

Continuing her series of interesting posts on the Historical Jesus, April DeConick today posts on Why the Jewish Jesus is Essential (and Dangerous). One element in it underlines the problems over the use of the term "the third quest" on which I commented in my post on abandoning the terminology of "the third quest". DeConick writes:

As I look back over the long history of the Jesus quest (and its popularized sidekick, Jesus in cinema), I continued to be struck (and I admit ashamed) that Jesus rarely appears as a Jew. There have been occasional voices over the last century that have demanded we remember that Jesus was Jewish, but these have been occasional and against the communal representations of Jesus that were developing in those eras.

And sadly this includes the Third Quest which largely has been trying to get around the fact that Jesus was Jewish by creating categories for Jesus as a Hellenized person living in Palestine or Galilee, but a person that doesn't look like any other Jew we know of who lived in Palestine or Galilee.

I am puzzled by this characterization of recent research. If there is one thing that the term "the third quest" has been associated with, I would say that that is stress on the fact that Jesus was a Jew. The pioneering works of the third quest, Vermes's Jesus the Jew and E. P. Sanders's Jesus and Judaism make this their major contribution to the extent that "Jew" and "Judaism" appears in the title. As Tom Wright characterizes "the third quest" (his term), he places Jesus as Jew as its defining element. I realize that DeConick is using the term "third quest" somewhat differently, and applying it to those like Crossan and Funk who are actually excluded from "the third quest" by Wright, but I think this further underlines the problem I was trying to bring forward the other day, that the term is becoming useless, or worse, confusing.