e.lat is a proper name used for a place rebuilt, restored, passed by, and inhabited in the cited verses.

The supplied occurrences use the proper name for a place: it is rebuilt and restored in 2 Kings 14:22 and 2 Kings 16:6, and it marks a route alongside Ezion-geber in Deuteronomy 2:8.

1. Place named in restoration and travel accounts · dominant

   All supplied forms are tagged Noun · Proper. In 2 Kings 14:22 the APB renders a clause in which it is rebuilt and restored to Judah; in 2 Kings 16:6 it is restored to Aram and becomes a place where others settle. In Deuteronomy 2:8 the APB renders it as a point on the route of the Arabah, alongside Ezion-geber.

   2 Kings 14:222 Kings 16:6Deuteronomy 2:8

In the Anselm Project Bible: The APB presents the name as “Elath” in all three verses, while also using “Eloth” in 2 Kings 16:6. That variation cannot by itself establish a different use of the Hebrew form.