One thing I have run into when looking into the Guanché Berber vocabulary is the word for 'sheep' tahaten. What is remarkable about this word (which is a plural), is that we find a written <h>. If we look at other Berber languages we find several forms of this word.
Tamasheq /h/ and Zénaga long vowels both come from the same origin, namely a Proto-Berber phoneme often reconstructed as *h or *β. I prefer the second reconstruction as the Ghadamsi reflex is b [β], it seems easier to explain a shift of [β] > [h] than the other way around. Besides Tamasheq/Tamazheq/Tamaheq (Touareg Berber), Zénaga and Ghadamsi Berber there is no evidence of this Proto-Berber phoneme, as you can see in the example of Tamazight, although, it might be possible that the long consonant tt is due to a cluster *βt.
Those three groups, Make up quite an archaic group of Berber languages, Zénaga retains Proto-Berber *ʔ. Ghadamsi Berber does to, though only indirectly. And all three groups retain an old phoneme *β. Zénaga is weird in other ways too, giving the impression that it probably split off before the other Berber languages.
So what does it mean that we find the word foor 'sheep' with an <h> in Guanché? Is the Berber that influence Guanché a Touareg language? That seems unlikely considering the geographical location. So maybe the consonant that gave rise to the long vowels in Zénaga was originally pronounced /h/ as well, geographically it makes more sense that a sister language of Zénaga was spoken by the Berbers that went to the Canary Islands.
Is this really the case? I have yet to run into other words that have a Proto-Berber *β in the root, which would be necessary to back up this idea. There's a good chance that, due to the limited material we have of this language, such a root will not be found. Which would mean that the pronunciation of tahaten either looks like a very Archaic Berber word by chance, or that we'll never know the answer.