Any Ideas on What the Sign of Jonah Was?

I have done a very detailed study on Jesus' resurrection and found some very interesting things. I even published a book 3 years ago: In the Heart of the Earth: The Secret Code That Reveals What Is In the Heart of God. But there are some details I feel I don't yet understand adequately. Perhaps someone can help me. The passages in question read:

"But he answered and said unto them, An evil and adulterous generation seeketh after a sign; and there shall no sign be given to it, but the sign of the prophet Jonas:  For as Jonas was three days and three nights in the whale’s belly; so shall the Son of man be three days and three nights in the heart of the earth." (Matt 12:39-40)

"And when the people were gathered thick together, he began to say, This is an evil generation: they seek a sign; and there shall no sign be given it, but the sign of Jonas the prophet.  For as Jonas was a sign unto the Ninevites, so shall also the Son of man be to this generation." (Luke 11:29-30)

And my reasoning and question is this:

Matt 11:39 says " there shall no sign be given to it, but ..." That implies one sign and one sign only. Many people when asked what was the sign of Jonah was reply that is was a sign that Jesus was the Messiah. But that can't be because there were many signs of that (the place of His birth, the time of His birth, the virgin birth, the many miracles He performed etc.) Clearly, it was a sign of something else - I think something very profound.

In addition, "the sign of Jonah" was a sign to the Ninevites not to the people of Jesus' generation. This is very clear from Luke 11:30. A key point to understand is that both passages say "as Jonas was ..." It is drawing a comparison between the two individuals and the respective signs. But we need to maintain the distinction. Whatever the sign of Jonah was, it was a sign to the people of Ninevah long before the time of Christ. The sign to the people of Jesus' day - "that wicked and adulterous generation (not the Ninevites)" - was clearly something different; different, but in some way similar. Perhaps it should be called the sign of the Son of man.

My book goes into the comparison and decides that understanding the "as;" the similarity is key. The passage is not focusing on the location (they were in different places) or the time. Indeed, a parallel verse does not even mention the time:

"For as Jonas was a sign unto the Ninevites, so shall also the Son of man be to this generation." (Luke 11:30)

It was not "where Jonas was so ..." or "as long as Jonas was so long ..." The focus is on the "as" on what was similar about their conditions. The book takes quite a different look at it, based exactly on what scripture says.

But to get to my question: in light of the above, what was the sign of Jonah to the Ninevites? Was there something about Jonah's experience that made a powerful impression on them? Some say he may have had his skin bleached from his time inside the whale. Was it his appearance? Did reports of his miraculous journey in the whale accompany him to Ninevah? How was Jonah a sign to the Ninevites? Does anyone have any clues or thoughts?