Bulent Ecevi university are looking at Cro-Inonu at Karadeniz Eregli in Zonguldak, near Heraclea Pontica. They've found signs of sentient life during around what would be the Hittite period.
This article from Türkiye Today is poorly edited. Although I do appreciate Gordon Doherty's map. Very late-1990s amateur 2e-D&D. I might have drawn some maps like that myself.
The region could be protoPhygrian (Thracian), or Mycenaean (Greek). I take it they've ruled out these cultures. Native to northwest Anatolia, this is about where I'd expect Palaic. Apparently they're ruling these out too. Left are those dirty woodwoses and troglodytes whom the Hittites named "Kaska", of whom all we know from their personal names is they're not Palaic or Greek.
I've heard musings the Kaskians might be the original Hatti; expelled from Hattus and Nerik (and Sapinuwa which just means "Divine City" in Hattic).
The problem I got is that even the map is suggesting that the Kaska clustered around the mouth of the Red River later named (after old Hattus) Halys, spreading east. Even Nerik was pretty far west of the core Kaska-land... which is why the Hittites were able to retake it. The cave is far westward of Nerik, across the river.