Anyone who has ever looked into Proto-Berber reconstruction, will have a great sense of déja vu, an important issue which is only getting a lot of attention now are the three Laryngeals of Proto-Berber, which we could conveniently call *h₁, *h₂ and *h₃, but unlike Proto-Indo-European, it is considerably easier to say something concrete about the original phonetics of these sounds.
The first person to write a considerable amount on these Laryngeals was Karl-G Prasse in his Manuel de graimmair touarègue (1974), which consists of three parts that extensively describe the Touareg dialects (and especially the Hoggar dialect) while constantly trying to reconstruct a Proto-Touareg and Proto-Berber with the forms he finds.
For utterly unfathomable reasons, he decides to lump all three laryngeals together and call them Proto-Berber *h and claims that the reflexes of this *h are the same, even though it is probably in origin multiple sounds. It is understandable that he overlooked the Proto-Berber *ʔ as very little was known at the time about Zénaga Berber which is the only dialect that reliable and clearly retains this laryngeal, but he must have known that the other two laryngelas were different.
Most dialects of Touareg clearly and unambiguously retain the distinction between the two h's. The first is retained as... you guessed it, Touareg h, while the other is retained as vowel length. He must have seen and known this, and even the PB *ʔ has clearly distinct different reflexes from the vowel-length h.
The Touareg h is at times reflected in other dialects as w and y and in Ghadamès & Aujila consistently as β, in Zénaga it is reflected as vowel length (it lost the Proto-Berber vowel length contrast).
These labial reflexes are hard to understand if we assume PB *h, so I think that it was originally PB *β. Now we have two Proto-Berber consonants in place PB *β and PB *ʔ. The third and last consonant PB *h is a lot more difficult to reconstruct.
In Berber standard trilateral verbs have the following conjugation
Aorist: ăC₁C₂əC₃ Perfect: əC₁C₂ăC₃ Intensive: C₁ăC₂C₂ăC₃
LMD = to learn, probably an early Punic loanword.
Aorist: ălməd Perfect: əlmăd Intensive: lămmăd [for an excellent discussion on this see also Lameen Souag's most recent post].
Lameen shows that there are some reflexes of the *ʔ I would like to look at the verbs that have the PB *h.
We find the verbal root GM (or according to prasse HGM) 'to draw water from a well'
Aorist: agəm Perfect: ugăm Intensive: ttagăm
Prasse would like to give a reconstruction as follows:
*ăhgəm Perfect: *əhgăm Intensive: hăggăm.
Clearly the system breaks down in the Intensive, but this may be the cause of some sort of analogy, but it is unclear to me how exactly he imagines this.
So a hidden laryngeal that triggers vowel lengthening (as a is the long counterpart of ă and u (and i sometimes) of ə). That sounds like *h₁!
But this, of course, betrays a predisposition to want to force verbal roots into triradical roots, because biradical roots are somehow unacceptable. We all know where this need comes from, we like to reconstruct Proto-Afro-Asiatic with a triradical root system, so it's quite problematic if a language that we want to belong to this language family (and with good reason) has a lot of biradical roots (and it does).
So from PAA we want to see it, but can we truly reconstruct it for PB? Isn't it preferable to say that an analogous system to the short vowel system happened in roots with a root vowel. You could, then look at Proto-Berber roots as having inherent vowels (or vowel length at least) and a root like GM would be better as VGM in a Proto-Berber dictionary.
We could then rewrite the tensconstruction vowel patterns as follows:
Aor: LOW-HIGH Perf: HIGH-LOW Intens: LOW-LOW
Just a little note on the Intensive construction that is attested, the vowel pattern is in fact correct (LOW-LOW), it's just the construction which breaks down is trying to fit the consonantal pattern in a triradical one (because it isn't?).
Of course, back in the days of de Saussure did exactly the same reconstruction of *h₁ as Prasse does with this PB *h, but I'm still not entirely convinced. For one, it does not get rid of all biradical roots in PB, not even in the verbal system (I think FL Lameen mentions is biradical not FHL), and definitely not in the Noun system.
The strongest argument for Prasse's theory is that I have not yet found any roots of the type VʔCC or VβCC, while theoretically there should be nothing against such constructions. But as Zénaga does not retain vowel length from Proto-Berber, this data could be extremely obscured by the language rather than a true absence.