My impression is that secular historians mostly just 'don't want to even go there'.
One reason I say that.....
"In respect to what I have called minimum demands there are good reasons for a historian to shrink from judgments on the historicity of the person of Jesus. This means, however, that the historian in this case, as in so many others, will say neither "The evidence is that he lived there and then" nor "The evidence is that he did not live there and then". The logical possibility of the existence of Jesus (at the religiously assumed place and time) cannot be denied, but the evidence seems to be too weak to give such a statement a minimum probability."
(Rolf Torstendahl, professor of history, Uppsala University, Sweden. From 2008 I believe).
Referred to in an interesting discussion (which I have only skimmed) here:
http://www.wikiwand.com/en/Talk:Historicity_of_Jesus/Archive_29
Full article from which I have copied and pasted the above quote can be retrieved here (link below) by clicking on
"Theologians as Historians" to download the pdf. It's an essay by Allvar Elleghrd (linguist by profession, also a writer on Christianity). Torstendahl's comments on it are near the end:
https://www.google.com/search?q=the...hrome..69i57.444j0j8&sourceid=chrome&ie=UTF-8
It must be noted that (a) ancient history is not Torstendahl's area of special interest and (b) he's expressing his personal opinion.
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My general impression is that among modern secular historians generally (there may be exceptions, but I myself do not know of many and can't think of any off the top of my head, other than Richard Carrier*), whether Jesus actually existed is what might be best described as an open question.
You might object to my making a distinction between religious scholars and historians per se, but I do think there is one to be made (although I would not in the end say they are two separate things or that a particular religious scholar is not an historian). I hope it's obvious I'm not discounting (as in considering unworthy of consideration) the work of either theologians or religious scholars, or even the views of anyone (including for example Jesus mythicists) just (ie only) because of potential cultural or other bias. Dispassionate, unbiased views on this, from either or all sides, are about as rare as hen's teeth, imo, and need to be taken into account and waded through. I almost certainly have biases myself.
But I will say this, in the case of reputable, academic religious scholars for example, and unlike most mythicists, at least the good ones know their historical subject matter in great detail, and of course there are, and have been over the years, a small minority among them who are very sceptical indeed about Jesus. Many New atheists have rallied to the latter's cause, sometimes a little too hastily, imo. Jesus is demonstrably still fascinating to many atheists nowadays. Threads about him have usually been among the longest ones, several of which I've enthusiastically participated in, on any atheist forum I've ever been on. And I admit that my own fascination is a little odd and somewhat ironic, or at least amusing (to me).
* A fool for buying into Earl Doherty's dodgy thesis, imo.