The question came up in this recent thread regarding Paul identifying himself as being from the tribe of Benjamin. The top response there makes no distinction between historical evidence and foundational mythology when telling the story of the Twelve Tribes, which at least from my understanding is likely more mythology than history. In that regard, I dug around and found Diana Vikander Edelman reasonably summarizing what I've gathered from Kings. In her The triumph of Elohim : from Yahwisms to Judaisms she explains:

It is fairly well established by now that the narrative of the book of Kings cannot be taken as an accurate reflection of the religious world of the nations of Judah and Israel. The cults of Jerusalem and Samaria appear therein as respectively, the repository of a proper religious tradition with lapses into heterodoxy and the fiendish creation of a sacrilegious traitor. This heterodoxy is portrayed by means of presenting those, wished to be denigrated by the author, as being worshippers of a pantheon rather than being loyal devotees of the one "true" God. As it is clear that the authors of the present material have a theological ax to grind, this picture should be seen as the product of an exilic or postexilic theology rather than a reflection of a real religious past.

Edelman then goes on to explain that Kings surely describes the time in which it was written to some extent, but I'm hoping a historian here can elaborate on how much of such scripture is corroborated by other evidence in the historical record. In particular I'm curious: how much prior to Paul's time can it be reasonably estimated that Israelites started seeing themselves as descendants of twelve distinct tribes?