Who were the Libyans?

A few years ago, I noted a conspiracy between the Libyans and the Sea Peoples as they made a play for Egypt. Yes, "Egypt": the pharaoh stopped them at the veriest house of Ptah; he altered his own name to "Merneptah", from that miracle. Today I'm pondering the Libyan side.

East Berber exists... today, and assuredly in Late Antiquity. I wonder however how long it has existed in western Egypt, or as far as classical Cyrene. Cyrene enters history when some Theran Greeks took it over and made it Doric. It then still had locals, perhaps the same locals as lived there during the Nineteenth Dynasty. But... who were they?

When did Awjila or old Tunisian Berber break off from the general Tamazight family? Nothing I see marks these languages as particularly deep in the tree, contrast Zenaga. In fact Awjila owns the same Punic verbs as the others.

If any "Nasamonese" was spoken there in Late Antiquity, it should, instead of Punic loans for literacy and technology, own Egyptian and Greek loans; allowing for some pre-Canaani Northwest "Amorite" Semitic. And structurally it should own some Zenaga-tier archaisms.

I must conclude that the Libyans were not Numidians and, whatever they spoke, might not have been Berber at all. It might have been some other branch of AfroAsiatic; it might have been paraEgyptian. I cannot even rule out that the Libyans in question, LBA to Early Iron, were simple Greeks, later to be Dorianised. We have evidence for Mycenaeans in old Sicily and South Italy; and of course Cyprus, maybe Pamphylia.

NEW CONCLUSION 3/28: Qeheq was Berber. We're at the stage of Libyco-Berber and the Canaries: enough consonant-inventory and syntax to assign it to the general Berber family; scarce on the actual, you know, words. Although, Awjili is no descendate of Qeheq.