At the private request from a forum member I am providing the following Jewish perspective to the question:
Does anyone know or does the Bible state when the Jonah story supposedly happen?
While the prophet Jonah is believed to be a historical person, the Biblical account is understood to be a satire.
The details are purposefully written to be either funny, preposterous, impossible or even outright silly to produce either:
1. A moral lesson for Jews to make them rethink their theology on being the only "chosen people" of God and the prejudices this produces as a result
2. A guide for prophets, teaching them how to do their job by teaching them how not to act and what attitudes not to have
3. Or a combination of the above.
Most Jewish scholars tend to favor the third view.
While Jonah is believed to be the historical author, it is impossible for him to have done any of the things mentioned in the book. Why?
1. Tarshish is a mythical place, and in the book of Jonah is merely a literary device meaning "a far away place." There was a pseudo-mythical harbor in Iberia that was washed away and became popular in Greek and Roman mythology, but it wasn't Spain which is mentioned by the reviewer (which I assume he got from the Watchtower).
2. Nineveh did not exist at the time of the book's composition. God's "sparing" it in Jonah's story is thus useless as it was eventually totally wiped away.
3. Jonah is the only prophet in the history of the Jews who is 100% successful in his assignment (at least in this written story) and over this Jonah pouts.
4. The book ends leaving the reader to question their views and beliefs, providing no answers nor the means to get them.
The story is basically a parable asking the Jews to reconsider their own views of uniqueness. Were we truly chosen by God to be his only people? Or were we just like every other ancient people who thought the same thing about their deity and place in the universe? When it came to bringing mercy to people of other nations, people who were not Jews, were they not just as deserving to the same? If God is truly the God of all, is not God's prophet the servant of all? Shouldn't we rejoice in the redemption of all instead of the condemnation of those who believe and worship differently?
Despite how you answer the narrative is not historical, at least not from a Jewish prospective.