ca. 8ky ago or so takes us back to the lifetime of TMRCA of proto-Tamazight/'Berber' speakers, the ancestors of contemporary Tamazight/'Berber' speakers.
Language differentiation of proto-Afrasan in Eastern Sahara-Sahel: These could have diverged into sub-branches of non-tonal proto-languages, which proceeded to expand northward, westward and south-eastward intra-continentally, while the north-eastward expansions culminated into the flow [of one at least] of these non-tonal proto-sub-languages, amongst other cultural elements, into the Levant to evolve into the Semitic languages of those regions. These would likely have been mainly E-M78 carriers. It is also possible that more than a single non-tonal proto-language branch made its way into the 'near East', i.e. possibly a few very closely related dialects making their way there [and not necessarily all at once], whereby they would have fused with one another to produce one or other several more Semitic languages, with fusions and fissions occurring over the course of history as groups interacted and others moved into new locations. Of course, some continued to develop throughout history ultimately into the languages as we know them today, while others likely became defunct at some point, even though they would have still shared common features with the surviving variety of today. Same thing could have happened intra-continentally, pending specific evidential corroboration to that extent. Apparently, other E-M35 lineages also made their way to “southwest Asia”, likely as far back, if not relatively little earlier than M78 derivatives [if Semino et al.’s 2004 chart is any indication], as evidenced by the Hg E-M123 across the Red Sea outside of Africa. What these people spoke when they reached “southwest Asia”, is anyone’s guess; it could likely have been some non-tonal sub-branch which, as the present author has said here before, mixed or what have you due to various demographic events of the region—just personal conjecture. These could have crossed at any point along the Red Sea, possibly even from sub-Saharan East Africa.
The tonal sub-branches of the differentiated parent proto-Afrasan language proceeded largely westward and south-eastward. Again, over the course of time, at some point in history, it is possible that some tonal proto-sub-branches became defunct or fused with one or several others to produce newer dialects, again—also not ruling out fusions and fissions of sub-branches as a product of interaction within proximity and movement to new locations ; just conjecture on the present author's part.
It goes without saying, that the above differentiation of proto-Afrasan basal language would not have been a single event, but a process [series of processes] which would have culminated in branching off at various points in time, and further differentiations within the Afrasan languages [i.e. in the sub-branches] would have been progressive as well, not single events.
Anyway, as far as proto-Tamazight speakers go:
If we are to keep in mind the above mentioned language “nature” and divergence of the Afrasan groups [with the help of insights from linguists like Ehret], along with lineage expansions, as observed by the likes of Underhill, Luis et al. [“Nile Valley vs. the African Horn”] and Arredi et al. (2004), not to mention Cruciani’s latest ‘re-organization’ attempts, then it would appear that the ancestors of the Tamazight/“Berber” groups diverged from within the general vicinity of between Egypt and Sudan expanse, or in the southern bound of the western [although the eastern desert cannot be ruled out in the assessment] desert of Egypt ca. 8ky ago or so, and thence moved northward, while others moved westward in the Saharan-Sahelian belts shortly after. By ca. 3ky ago sections of these earlier “Berber” populations would have expanded westward, culminating in considerable expansions in the westernmost coastal North African regions by 2ky ago or so [Luis et al. 2004], resulting from what became a 'founder effect' in that region.
Throughout prehistory and history, some of these more mobile Tamazight/“Berber” groups, like those in the Sahel and the Sahara, may have moved back and forth, i.e. from the north back to the Saharan regions and vice versa. For instance, it isn’t surprising that Saharan/Sahelian Tamazight/“Berber” groups like the Sanhaja closely resemble sections of northern coastal-based groups like the Kesra of Tunisia, and indeed, the Sahelian Tamzight/“Berber” groups have a history of setting up socio-cultural complexes or “empires” in coastal North Africa by way of conquests. It would appear that the Tamazight/“Berber” groups likely diverged from the same populations ancestral to the contemporary Bedawi in the Red Hills regions of Sudan [e.g. see above: Underhill for indicators].
The Beja language, which is viewed by some linguists to be a somewhat distant relative of Cushitic languages, is perceived to be relatively closer to the non-tonal Egyptic, and other [generally perceived] younger non-tonal branches of “Berber” and “Semitic” than the largely tonal Afrasan groups in sub-Saharan east Africa. The Chadic branches, which are perceived to be largely tonal, undoubtedly have some level of closeness with Tamazight/“Berber” languages given the proximity and interactions of these groups in the Saharan-Sahel regions…just as Ethio-semitic languages have some level of closeness with the Cushitic languages therein due to years of interaction and cohabitation.
According to Underhill, E-M81 appears in samples from Sudan, wherein it occurred in two individuals who happened to be of Beja extraction...
Apparently, Arredi et al. (2204) also took note of this finding, as relayed by Underhill:
Second, just two haplogroups predominate within North Africa, together making up almost two-thirds of the male lineages: E3b2 and J* (42% and 20%, respectively). E3b2 is rare outside North Africa (Cruciani et al. 2004; Semino et al. 2004 and references therein), and is otherwise known only from Mali, Niger, and Sudan to the immediate south, and the Near East and Southern Europe at very low frequencies....
The M35 lineage (see the phylogeny in fig. 1A for marker locations) is thought to have arisen in East Africa, on the basis of its high frequency and diversity there (Cruciani et al. 2004; Semino et al. 2004), and to have given rise to M81 in North Africa. The TMRCA....E3b2 (2.8-8.2 KY) should thus bracket the spread of E3b2 in North Africa.....Thus, although Moroccan Y lineages were interpreted as having a predominantly Upper Paleolithic origin from East Africa (Bosch et al. 2001), according to our TMRCA estimates, no populations within the North African samples analyzed here have a substantial Paleolithic contribution.....In addition, genetic evidence shows that E3b2 is rare in the Middle East (Semino et al. 2004), making the Arabs an unlikely source for this frequent North African lineage. — Arredi et al., A Predominantly Neolithic Origin for Y-Chromosomal DNA Variation in North Africa
SNP Haplogroup Frequencies in the Five North African Population Samples and Other Published Samples: http://www.journals.uchicago.edu/AJHG/journal/issues/v75n2/41184/41184.html
Those regions accompanied by Sudan above, in particular those in "Near East" and "Southern Europe", are largely areas where Imazighen (Berbers) groups have historically emigrated to. However, since I'm not aware of any notable Imazighen (Berber) presence in Sudan, although the Siwa "Berbers" do reside in the northwestern desert of Egypt, E-M81 detection therein, must be a relic of groups ancestral to the aboriginal Imazighen populations [who have become more or less modified to varying degrees, by gene flow with neighboring non-Imazighen populations, whether it is in the Sahara and Sahel, or right across the Mediterranean Sea], who generally happen to be genealogically tied by the aforementioned E-M81 marker — hence, its nickname as a "characteristic Berber" marker.