Marijn van Putten lately uploaded his work on protoBerber roots. They are called "Berber" after the Greek mockery of those who speak poor Greek, I think starting with the Macedonians in their days (cf. Pherenike v. Mac. Berenice). Most indigenous Saharans tend to call themselves, er, the Fremen.
As others witnessed the Imazighen, so the Imazighen learnt from others. The Arabian dromedary must be a case in point (I don't think the old African camel was remembered). I have in mind here the stem əlməd. Van Putten sets this word first on his list, which is nonalphabetic; it boasts pride of place, for him. This əlməd means "to learn". Any Jew - who are just G-d fearing punici - can tell you lmd bore the same understanding in old Canaanite. An Arab would have his own terms like 'rf and 'lm.
Immediately to my attention is that əlməd isn't in Sanhaja / Zenaga. Van Putten uses Zenaga copiously elsewhere. Also the Zenaga in Mauretania today are proud scholars of (Islamic) literacy. They absolutely have words for learning, and van Putten absolutely would know those words. The Zenaga have simply chosen not to use this word.
I submit that the Sahara got əlməd from the incoming Canaanites, after the Zenaga went their own way. This would have happened during or after the Third Phase in Morocco. It is difficult to pinpoint further on account the Kabyle, who may have split during the Bronze Age, continued contact with the wider Med even where not with fellow Berbers. They could have taken the root on their own, as Syriac and Coptic will each take from Christian Greek.
I wonder how many other Punic words are hiding in the deep lexicon, ignored because they look Arabic so late.