I think they've got no clue about languages spoken at either site, and it will probably remain that way. Imagine what it would take -- there would have to be a body of inscriptions contemporary with a site; a bilingual text, both unreadable, but one a later successor tongue, which also has some sort of body of inscriptions at some site or sites; then another bilingual inscription with a third successor; and this sequence would have to repeat until the newer language on the bilingual were one someone knows how to read.
Here's one of my favorite clippings for reprise -- there are short inscriptions in the European cave paintings:
In her Plato Prehistorian: 10,000 to 5000 B.C. Myth, Religion, Archaeology, Mary Settegast reproduces a table which shows four runic character sets; a is Upper Paleolithic (found among the cave paintings), b is Indus Valley script, c is Greek (western branch), and d is the Scandinavian runic alphabet.
Thanks for the followup on my question re: language. A written language would likely be revolutionary.
On the subject of cave paintings here is a bit of an editorial of mine about the archaeological history of that {near the bottom of the page}.
My views on hunter-gatherers taking two millennia to build Göbekli Tepe can be read here. I have compared such to the building of the British Parliament building in the time of Julius Caesar and being finished about WWII; think of all the changes that took place over that period.