The fish incident is just one data point, and if it were excised from Jonah there would still be good reason to think of it as non-historical. The narrative is saturated with melodrama, scripted extremes, and even farce for emphasis:
- God’s order to Jonah to go and, sincerely and passionately, preach repentance to Israel’s worst of the worst: Nineveh
- Jonah’s flight in the exact opposite direction of Nineveh - even to the ends of the earth (a boat headed for the far western Mediterranean)
- The casting of lots and Jonah resignedly letting himself be tossed overboard (whence the sea immediately calms)
- Jonah’s long, wordy, elegant, thoughtful, beautiful poem - all carefully composed and spoken and yet whilst in the direst of straights
- God: “OK let’s try this one more time”
- Jonah’s subsequent sermon in Nineveh - the world’s shortest ever, just a handful of words
- And nonetheless, the Ninevites’ immediate, over-the-top acceptance of the message (Jonah’s worst dream come true, on steroids)
- Even the animals of Nineveh repenting in sackcloth
- Jonah: “Oh God just kill me now”
- Then the miraculous plant - and suddenly Jonah’s all happy!
- But then the plant dying - and suddenly Jonah’s a wreck again (the world’s greatest drama queen)
- And the story finally ending on the punch-line, the takeaway, straight from God
Real history never unfolds in such repeatedly and consistently melodramatic, farcical fashion, as that.
Oh, and there’s the fact there is no historical record of such a mass conversion in Ninevah, and no mention of chronological specifics in Jonah either (unlike regularly found in the other prophetic books - the name of the king of Ninevah, for example, or of the kings at the time in Samaria or Jerusalem).
So, this is a cumulative case, and the bit about the fish is just one part of it; leaving it out from the above makes virtually no difference.