There are so many different reconstructions of the historical Jesus, each one only an approximation of what the historian can know on the basis of the extant sources. There are lots of historical Jesuses that I do not believe in. I don't believe in Crossan's historical Jesus because I don't believe in his sources. I don't believe in Wright's historical Jesus because he believes all his sources. I don't believe in Morton Smith's historical Jesus because he composed one of his sources.
... doing ancient history is not like doing modern history. The vast majority of ordinary punters made no impact on the archaeological record from antiquity. Their impact, their "existence", if you like, can only be measured in so far as they influenced the memories of those who told their stories, and only in so far as those embellished, interpreted, creative memories ultimately found their way into the texts that managed to survive.Well worth reading the whole thing.