In the Gospels, the basic temporal structure of Jesus' personal storyline revolves around the fate of John the Baptist, and from that basic story structure -- not "narrative structure" (discoursed sequence of telling) but "story structure" (logical sequence of natural contingencies) -- we can extract the indisputable outline upon which to construct Jesus' historical event sequence. This "extraction" is a critical task, fundamentally unlike the textual blending of religious harmonizations. This requires distinguishing between text and content. Historicity is another issue, which I suspend for the moment. As truth or as fiction, the pattern of basic contingencies in the "story content" of the Gospels revolves around John the Baptist as follows:
Phase 1: before John's arrest.
Phase 2: during John's imprisonment.
Phase 3: after John's beheading
The story world of the Synoptics is portrayed consistently in each of these phases with distinctly different aspects of represented historical context. Before John's arrest, Jesus remains obscure and misunderstood despite making memorable introductions, and he stays mainly in Judea. During John's imprisonment, Jesus' popularity swells along with his travel schedule and the size of the crowds that so frequently assemble around him. The disciples cement their allegiance and significant controversies develop, but Jesus continues to move freely about Galilee unmolested. After John's beheading, Jesus travels widely outside Galilee to the east, west and north, clearly avoiding Herod Antipas' reach and yet avoiding Judea until the point at which (for whatever reason) he embraces that danger, heading straight for Jerusalem.
The story world of the fourth Gospel can be integrated (not "harmonized") with this "Informal Timeline" by recognizing the one event (prior to Jesus' passion) which the four canonical Gospels all represent - the feeding of the 5,000 near Bethsaida. If the writer of John (and his audience) remember Mark's account of John the Baptist's basic storyline, then we may compare the contextual details of all four narratives of this purported feeding. This aligns Phase 3 with the purported events represented by GJohn 6ff, and the characteristics listed above run in parallel with this content. Obviously, Phase 3 receives the most attention from all four Gospels by including the events of Jesus final passion in Jerusalem.
To align the story content of GJohn with Phases 1 & 2 we merely need to infer that GJohn intended 4:1-3 to invoke John's arrest by evoking the basic idea that Jesus entered his period of public ministry in Galilee at about the same time John was arrested. Apart from the explicit references to this "event" at Mark 1:14 & Matthew 4:12, the basic idea that Jesus "came after" John is attested recurrently throughout all four Gospels. In this simplified story sequence I find a rough approximation of social memory about Jesus' public debut. We also find a basic correlation of Jesus' Galilean ministry with John's imprisonment in the content of several Gospel traditions which the writers logically placed in "Phase Two". The most notable of these traditions, obviously, is in Matthew 11 = Luke 7, where John sends Jesus a question from prison. Overall, therefore, a substantial pattern of information across the tradition makes it plausible that John 4:1-3 marks a deliberate and plausibly effective invocation of the idea that John's arrest is what prompted Jesus' move into Galilee.
On this basis, the time periods which I've labeled as Phases 1 and 2 are aligned with the events represented by GJohn 1-3 and 4-5, respectively. Once again, the contextual distinctions between phases are consistent with this division of content. Whether historical or fictional, GJohn's representation of Jesus' activity corresponds to the same pattern of three temporal phases as all three Synoptics.
We have now successfully extracted from the four Gospels, by critical analysis, a basic sequence of represented events which uniformly aligns each of their literary representations with a single historical background - namely, the famous fate of John the Baptist, as also attested by Josephus. Rather than harmonizing parallel sequences of narrative discourse and mapping those sequences onto one another, we have selected content which similarly reflects the changes in the represented "status quo" which arise in the story world(s) in a logical ordering due to natural contingencies. Note, again, the question of historicity remains suspended. Whether fiction or non-fiction, the Gospel writers have constructed historical representations of Jesus' public activity, and they have deliberately sequenced their tellings to align with the historical events of John's arrest and beheading. To put that another way, when the Gospel writers decided to include a particular tradition in each of their narratives, they sequenced that episode according to whether it logically fit before John's arrest, during John's imprisonment, or after John's beheading.
The only possible exception to this is the "Temple Incident", but I would argue that Jesus most likely took that action once in his earliest ministry phase and did so with relative impunity - simply because he was an unknown entity, not yet considered a political threat - and then repeated that action on his final trip to Jerusalem, either by having the identical response to an identical stimuli as before, or perhaps in a deliberate effort to remind the authorities of his earlier action. Indeed, we might take my demonstration here of these writers' historical awareness (about representing events according to the contextual distinctions between these three phases of Jesus' ministry) as evidence that the beloved disciple was unlikely to "relocate" an event from Phase 3 to Phase 1. But in any event, there is no other event placement that falls outside of these placements. Events told "out of order" in Mark and Matthew fall within the same Phases, and the material which Luke lifts and moves into his travelogue would not cause his audience to sense problems in continuity because it naturally makes sense that famous sayings could have been repeated on multiple occasions in various contexts. (Also, Mark Matson argued at SBL 2016 that Luke cues his audience to take the travelogue as a timeless section of narrative, a.k.a. essentially fictitious.)
There is one last related issue to discuss. Three phases of Jesus' public ministry can be aligned with John's three references to the annual Passover as follows. If the feeding of the 5,000 is taken a composite event (which I would argue it was in the minds of John's audience), then we may reasonably infer that John's beheading was understood to have happened just before the Passover season at which (apparently) 5,000 Jewish pilgrims sought out Jesus instead of going to Jerusalem (John 6:4). Similarly, the Passover of John 2 falls somewhere during Phase 1 and Jesus' final Passover obviously falls at the end of Phase 3. The implications of this will be instructive for working from this "critically extracted event sequence" towards any formal chronology of Jesus' public ministry.
If we accept the historicity of these three Passovers, we must also recognize there could have been more than three Passovers altogether, during the three phases of Jesus' public ministry. Accepting these three as the only three is the chief fallacy of positivistic historicism, but a properly historiographical inquiry does not equate textual representation with the entirety of the past. So then, we are led to ask two surprising questions about the timeline of Jesus' historical ministry. Note again, the following question assumes nothing about the historicity of specific content placed by Gospel writers into Phases 1, 2, and 3, but it does assume the historicity of John 6:4, which remembers the beheading in alignment with one particular Passover feast.
Here are the questions:
(1) How long was John's imprisonment?
(2) How long after John's death was Jesus' death?
Answering the second question is more straightforward than the first. We've accepted that Phase 3 stretches from the Passover of John 6:4 until the Passover of Jesus' crucifixion, but that doesn't mean Phase 3 lasted for exactly one year. It could have been two years, or three years. Could it have been four years? This is a new question and deserves future attention.
Similarly, we've accepted that John's imprisonment ends just before the Passover of John 6:4 and begins sometime after the Passover of John 2, but that doesn't mean these two Passovers took place in successive years. If that was the case, we'd say John's imprisonment lasted for less than one year, but it could have been 1 to 2 years, or 2 to 3 years, or 3 to 4 years. Again, the limit of this inquiry is a subject for future discussion.
Altogether, if Jesus' baptism happens sometime before the Passover of John 2, then his entire public ministry might have spanned a bit more than two years, or a bit more than 3 years, or a bit more than 4 years, and so on. Once more, the upward limit is unclear, but the significant contribution of this reasoning is that the larger question can be subdivided. Rather than merely asking about the length of Jesus' ministry, we can also consider the length of John's imprisonment and how long Jesus lasted after John was beheaded. These are interesting questions in their own right because they could help to contextualize the literary material (or whatever is granted some degree of historicity in literary material) which the Gospel writers place into Phase 1, and Phase 2, and Phase 3.
In closing, I feel the need to emphasize once more that we do not wave magic wands over passages of narrative and thereby map events into chronology. For instance, the micro-sequences of the material placed in Phase 2 remain historically (that is, chronologically) in question even IF all such material is granted full historicity. Likewise, the micro-sequences of events represented during Phases 1 and 3 must be considered a separate problem. There may be other natural contingencies to consider, like the development of Jesus' relationship with his disciples, and their curiously variable levels of commitment to him, but these are questions for a deeper round of inquiries. In any case, such inquiries should attempt critical extraction of logical sequences according to natural contingencies - just as we have done here with the progressive misfortunes of John the Baptist.
It is one thing to accept narrative content as historical and quite another to deal with narrated sequences. Content must be analyzed by historical thinking, not merely by mapping an order of discourse onto the imaginable past. In addition, we have (at this point) not yet begun to consider what calendrical dates might be attached to any of these event sequences. There is much more work to be done.