Betar is mentioned in the Masoretic Text

[Update Feburary 5th 2025: This theory is defunct since I now know the name of Betharabah points to the Arabah plain.  Also the Archeology for Betar only goes back to the 700s BC so indeed probably isn't in Joshua 15.  A Betaris is mentioned by Josephus in Wars Book IV Chapter 8 but he placed it in the midst of Idumea next to Caphartobas so can't be the same Betar, it's likely a scribal error for Begabris.  

Rather it could be one of the cities built in the Mountains of Judah by King Jotham in 2 Chronicles 27:4, or perhaps have it's roots in Uzziah's projects from 26:10.  Based on what The Talmud says it seems Betar was a name given to this city because of The Bar-Kochba Revolt and so wouldn't be it's Biblical name.  

My hunch has become that Betar's Biblical name was Etam considering it's close proximity to Bethlehem and Tekoa in 2 Chronicles 11:6, in Judges 15 Etam isn't a city and in 1 Chronicles 4 it's only a village so it's history as a fortified city could begin with Rehoboam.  The area people are conventionally looking for Etam is lacks any Iron Age fortified ruins, and the Spring near Solomon's Pools currently named after Etam I believe is The Biblical Gihon]

Betar is an Ancient Israelite City located near the modern settlements of Battir and Beitar Illit most famous for having been the main base of operation of Simon Bar-Kochba during the Bar-Kochba Revolt.

Its Wikipedia Page talks about how there is archaeological evidence of its existence during the Iron Age yet says it isn’t mentioned in The Masoretic Text of the Hebrew Bible only specifically the Sinaitic Text of the Septuagint for Joshua 15:59a.

However The Masoretic Text and thus The King James Bible do mention a city in Joshua 15 and 18 who’s name can easily have been later shortened to Betar, Betharabah.

In Joshua 15:6 it is associated with the border of the land allotted to Judah, and then in Joshua 15:61 it’s described as being in a “Wilderness” right after talking about Kirjathjearim. But the name is also given to a Benjamite city in Joshua 18:22.

Betar’s location can be described as both between Kirjathjearim and Jerusalem and as between Kirjathjearim and Bethlehem.  So it is in a good place for being associated with both Benjamin and Judah.