Millard Erickson channels his inner Bruce Ware to argue that if God gives timeframes about the future, then the future does not have freewill choices:

Here again, however, a feature of the narrative presents a problem for the open theist position. Bruce Ware in particular points out that Jehovah does not just tell Hezekiah that he will extend his life. He is much more specific: his life will be extended by fifteen years. Ware says:

Does it not seem a bit odd that this favorite text of open theists, which purportedly demonstrates that God does not know the future and so changes his mind when Hezekiah prays, also shows that God knows precisely and exactly how much longer Hezekiah will live? On openness grounds, how could God know this? Over a fifteen-year time span, the contingencies are staggering! The number of future freewill choices, made by Hezekiah and by innumerable others, that relate to Hezekiah’s life and well-being, none of which God knows (in the openness view), is enormous. 19

Erickson, Millard J.; Erickson, Millard J. (2009-08-30). What Does God Know and When Does He Know It?: The Current Controversy over Divine Foreknowledge (p. 24). Zondervan. Kindle Edition.

Erickson does not discuss any Open Theist counters to his point, but many can be easily imagined. Both “God’s protection” and “predictable probabilities” are two possible answers. A third that will be developed in this response is that often in the Bible a timeframe is given and that timeframe is only a loose estimate, sometimes off by decades. The pliability of predicted timeframes is both good evidence that the future is not known and good evidence that in the case of Hezekiah, that the timeframe did not have to be exact to still be fulfilled.

Two loose predictions that will be discussed are the Babylonian exile and the captivity in Egypt. In Genesis 15, God promises Abraham that Israel will be oppressed in Egypt for 400 years:

Gen 15:13 Then the LORD said to Abram, “Know for certain that your offspring will be sojourners in a land that is not theirs and will be servants there, and they will be afflicted for four hundred years.

There is a specific and divergent number given in an Exodus text:

Exo 12:40 The time that the people of Israel lived in Egypt was 430 years.
Exo 12:41 At the end of 430 years, on that very day, all the hosts of the LORD went out from the land of Egypt.

Here is Answers in Genesis trying to answer the problematic numbers (they attempt to start the 400 years of persecution with Ismael mocking Isaac!). Not very persuasive. It is more likely the numbers are ballparks and not absolute.
https://answersingenesis.org/bible-questions/how-long-were-the-israelites-in-egypt/

The next event at which we will look is the Babylonian captivity. Christine Hayes writes:

Notice that the decree at the very beginning in Chronicles — in the 2 Chronicles version — the decree is said to fulfill the word of the prophet Jeremiah. Now, you remember that Jeremiah prophesied that the Babylonian exile would last 70 years; he wrote a letter, he said settle down, this is going to last a while, plant plants and build homes. So he had prophesied 70 years for an exile. Well, from the time of the first departure of exiles in 597, maybe to the return in 538, 61 years — it’s close. If you look from the destruction of the first temple perhaps in 586 to the completion of the second somewhere between 520, 515, we’re not really sure, that’s about 70 years. Either way, it seems that in the eyes of the Chronicler it was close enough. This seems to have been a fulfillment of Jeremiah’s prediction. That it would be about 70 years before they would return.

One site attempts to claim that the 70 years applies not to the judgment Israel but to a judgment against Assyrian. But to the author of Daniel, 70 years of desolation was applied to Israel:

Dan 9:1 In the first year of Darius the son of Ahasuerus, of the lineage of the Medes, who was made king over the realm of the Chaldeans—
Dan 9:2 in the first year of his reign I, Daniel, understood by the books the number of the years specified by the word of the LORD through Jeremiah the prophet, that He would accomplish seventy years in the desolations of Jerusalem.

Either way, the Babylonian exile and the Egyptian captivity present major problems and inspire from apologists all sorts of clever ways to avoid the problems. Surely, if Hezekiah ended up dying in only 5 years, all sorts of similar apologetics would spring up (“Maybe the 14 years is counting from a time Hezekiah would have died if not for the foreknown repentance”). These explanations, much like the attempted explanations of the Babylonian and Egyptian captivities, stretch credulity.

In the Bible, prophecy is often not exact even when using precise numbers. This is because the future is not known, and leeway is allowed. These loose timeframes, contrary to being evidence against Open Theism, is evidence for Open Theism.