In 1 Chronicles 3:15 we find a list of king Josiah's four sons:
The sons of Josiah:
Johanan the firstborn,
Jehoiakim the second son,
Zedekiah the third,
Shallum the fourth.
Then in Jeremiah 22:11-12
or this is what the Lord says about Shallum son of Josiah, who succeeded his father as king of Judah but has gone from this place: “He will never return. 12 He will die in the place where they have led him captive; he will not see this land again.
We have no record of a certain Judean king Shallum, he is not listed in the Book of Kings, or anywhere else besides for the reference in Jeremiah. This has led commentators to speculate that Shallum is Zedekiah son of Josiah, or perhaps Jehoiachin his grandson, or maybe Jehoahaz the predecessor of Jehoiakim, and a son of Josiah. As recorded in the Book of Kings, Pharaoh Neco captured him and brought him to Egypt where he eventually died. Thus Jeremiah's prophecy would have been fulfilled.
Almost all encyclopedias and scholarly sources accept the opinion that Jehoahaz is Shallum, Josiah's fourth son. This strikes me as odd, it seems unlikely that the fourth son of Josaih would have served as king before the second oldest son Jehoiakim has served (Johanan the oldest we have no record as ever serving as king. The LXX has Jehoahaz instead of Johanan as the oldest). But all sources tout this idea that Shallum and Jehoahaz are the same person without providing any evidence! As I pointed out earlier, Shallum can be any of the other two sons or maybe even a grandson of Josiah (either Jehoiakim or Zedekiah fit the description of Jeremiah's prophecy perfectly, they both died in Babylon), or he could be none of the above, and though it is unlikely it is not impossible to suppose that Shallum indeed served after Zedekiah was deported, or sometime between Jehoiakim and Zedekiah or Jehoahaz's reign for just a few days!
So what biblical or extrabiblical evidence do we have to support the theory that Shallum is Jehoahaz?