I wrote in The Archaeology of Armageddon:

The site was occupied almost continuously from about 3500 BCE until about 586 BCE, but a direct connection to King Solomon has yet to be found. What were thought to be Solomon’s stables now seem to date from the reign of Ahab, about 870-850 BCE. Ahab and his father Omri get a terrible press in the Biblical book of 1 Kings, but unlike their predecessors in both Israel and Judah, they are mentioned in contemporary Moabite and Assyrian records. We do not yet have such a verification of the Biblical account for David and Solomon

However, somebody at that time was operating a large copper mine in what is now Israel with fortifications. Radiocarbon dates these mines to the 10th century BCE, the presumed era of David and Solomon. The site is between the ancient Kingdom of Israel and that of Edom, and possession was probably disputed. 2 Sam. 8:13–14:

David won a name for himself. When he returned, he killed eighteen thousand Edomites[a] in the Valley of Salt. He put garrisons in Edom; throughout all Edom he put garrisons, and all the Edomites became David’s servants. And the Lord gave victory to David wherever he went.

So Timna, with its fortifications, may have been one of the places that David garrisoned. The war with Edom may have been partly about control of these valuable mines.

No written records have been found at the site, so we cannot definitely say that these were David’s or Solomon’s mines, but the date is right. Also, fiber fragments dyed with Tyrian purple have been found there. Technical details at Early evidence of royal purple dyed textile from Timna Valley (Israel). Hence there was someoe very powerful and enormously wealthy on site at that time.

There is still no trace of the palaces of David and Solomon. But archeologists may have found a lot of their industrial waste, and traces of clothing worn by one of them or a close associate.