An argument for the historicity of the Gospels that deserves attention is the argument from the reticence of the evangelists. Here's, in outline, how it goes: Consider the hypothesis that the Gospels are, or include, later, legendary stories. Then look at various places where human curiosity is not gratified in the Gospels by added stories, where one might expect these if the Gospel authors were not constrained by their actual knowledge or the information they got from real sources close to the facts.
This argument is closely related to the apparent reticence of the Gospel authors to "read back in" theological interests into early material.
Here are several categories of stories that we might expect to find if the Gospel authors were not constrained by truthfulness and available information, but that we don't find:
--Later stories about Joseph, Jesus' guardian. Joseph is a very sympathetic character. Why does he just disappear after the narratives of Jesus' infancy and the one story in Luke about Jesus in the Temple at age twelve? In my forthcoming book, I argue that Joseph "disappears" because he actually did disappear--that is, that he died prior to the beginning of Jesus' ministry. But this is, at most, implied. No Gospel actually mentions Joseph's death. It would have been easy enough for the author of John, say, to come along and add stories about Joseph later on, either before the beginning of Jesus' ministry or during Jesus' ministry. But he doesn't. Joseph is also conspicuously absent from many passages that explicitly mention, in a list-like fashion, Jesus' family members. The best explanation for this combination of presence and absence (the presence of Jesus' family, listed, and the absence of Joseph) is that Joseph wasn't around at all in those scenes and that the Gospel authors are truthfully reflecting that fact.
--Accounts of Jesus' post-resurrection appearances to James and Peter. This is quite surprising, when you think about it. The much-cited creedal formula at the beginning of I Corinthians 15 shows that the appearances to James and Peter were well-known in the Christian community at a very early date and were considered important to the Christian faith. Yet the Gospels, which are sometimes treated (even by relatively conservative scholars) as less reliable than the Pauline creed in I Corinthians, do not include anywhere in their appearance accounts any scene showing these meetings. Luke contains a mention (in dialogue) of the fact that "the Lord...has appeared to Cephas," but no developed scene at all (Luke 24:33). No Gospel even mentions the separate appearance to James, Jesus' kinsman. If the Gospels contained developed, legendary tales, these scenes would be perfect for inclusion. If Christians were sitting around making things vivid to each other, or to their children, by "fleshing out" the bare bones of the claim that Jesus (somehow, sans details) appeared to his disciples, one would assume that the scene of the appearances to Peter and James would be thus fleshed out. But if that was going on, we certainly see no sign of it in the Gospels.
This makes sense if the Gospels are constrained by honest reportage. Both Peter and James had reason to keep the details of such meetings private. John records that Jesus' brothers did not believe on him (John 7:5). The first we hear of the prominence of James (this is not James the son of Zebedee but James the kinsman of Jesus) in the Bible is in the book of Acts. It seems that James may not have believed on Jesus at all until the post-resurrection appearance. Peter, of course, had denied Jesus even after insisting that he would do no such thing. Their first meeting after Jesus' resurrection would have been extremely important to Peter, personally, but he may well not have wanted to tell exactly what was said. Real people often do refuse to share particular details. Sometimes they tell others that certain details are "not for publication." The absence of accounts of Peter's and James's first meetings with Jesus is easily explained if the Gospels are accounts coming from eyewitnesses or those close to eyewitnesses who are not including anything that they don't actually know to be true or don't have authorization to publish. This reticence is much harder to explain if the Gospels are unreliable documents that include non-factual stories that "developed."
--More information about Jesus' childhood. We're all curious about Jesus' childhood. Could he do miracles? How did he come to know that he was God as he grew up? How did he and Mary talk with each other? Later documents and, more recently, movies have explored these questions, but the canonical Gospels are extremely restrained. The only scene that even touches on such questions is the Temple scene in Luke 2. Both before and after that, Jesus' childhood after his infancy is left unknown. And the same for Jesus' young manhood prior to the beginning of his ministry. Again, this restraint is far more to be expected from honest reporters who stick to what they know than from recorders (or inventors) of pious legend. The earliest chapters of Luke, which contain the scene in the Temple, have a strongly Hebraic character and style quite different from Luke's usual style, which begins in Luke 3:1. I generally hesitate to hypothesize documentary sources, but it seems plausible that in this particular case there really was an earlier document that Luke translated, possibly given to him by Mary's family. But in that case he included nothing more because this was all the reliable information he had.
Here are a few of the instances of theological reticence:
--The presence in the Annunciation of references to Jesus' reign as the heir of David, combined with the absence of any allusion by the angel to his suffering and death. See a post that discusses this further (at the end of the post) here. This is much better explained if the Annunciation is taken, by Luke, from information he actually had about what was said than if Luke made up the scene. Luke himself obviously knew that Jesus never inaugurated an earthly reign, yet the intensely Jewish expectation encouraged by the angel's message and reflected in the Song of Zechariah would most naturally be taken to refer to an earthly reign of the Messiah. The Gospel includes no comment on or qualification of this expectation in these chapters. It just records what was allegedly said. This is good evidence that these chapters are not late developments but rather very early information not at all influenced by later knowledge or preoccupations.
--The absence of the Great Commission or any other endorsement of Christian baptism in the Gospel of Luke, combined with the extreme importance of baptism in Acts, written by the same author. It is possible that Luke didn't have access to Matthew, though I myself think it is highly likely that he did. (Nor is that some kind of fringe, "conservative" opinion, though I gather scholars are not unanimous on whether Luke or Matthew was written before the other.) If Luke had access to Matthew, and if Luke were trying to include things in his own Gospel for literary or theological purposes, it is quite remarkable that he didn't include the Great Commission. It is all the more remarkable given that the author of Acts (universally acknowledged to be the same as the author of Luke, though not universally acknowledged to be Luke) is keenly aware of the importance of baptism in the early church and records its importance from the day of Pentecost onward. Similarly, the Gospel of John records in John 4 that Jesus' disciples baptized, but the Gospel of Luke never mentions any such claim. If these stories were going around, wouldn't Luke have wanted to "set up" the importance of baptism in Acts? (This argument is modified from Stanley Leathes, The Religion of the Christ, 1874, pp. 257-258. Thanks to Esteemed Husband for bringing it to my attention.)
I hasten to add that I don't mean by this to cast doubt on the historicity of the Great Commission or of Jesus' disciples' baptizing ministry recorded in John 4. My point, rather, is that it is clear that the Gospel of Luke is not trying to record everything and not even trying to record everything that could be useful theologically. For all its high Greek language, the Gospel of Luke, like the other Gospels, has the quality of reportage rather than of literary crafting.
The Gospel authors are so far from putting words into the mouths of Jesus and/or his disciples for literary, legendary, or theological purposes that there is something, in a sense, slightly random about their including some incidents and not others. This is what we expect from a writer collecting living history from witnesses, or a witness himself, and writing a memoir.