It's true that E-V13 has a mind-boggling distribution pattern that doesn't get much clearer when looking at subclades. That has to do with the fact that this lineage expanded very quickly from a single ancestor living at the onset of the Bronze Age and that E-V13 probably expanded with all Indo-European branches, so that branches can be Indo-Iranian, Balto-Slavic, Mycenaean, Illyrian, Italo-Celtic, and Germanic. To make it worse, it appears that some people, like the Hallstatt Celts, the Romans and the Goths redistributed some clades across wide geographical areas and mixing them with others.
Everything would look clearer if we had sufficient data for deep clades. Unfortunately a lot of people only tested at a level corresponding to the Middle Bronze Age, before the ethnogenesis of most historical people took place. What we need is data at least at the Iron Age or Classical Antiquity level, especially for southern Europe. Other haplogroups like I1, I2, N1c, R1a and R1b have a much higher phylogenetic definition, which makes it possible to trace back historical population movements. With E-V13 all we can do now is guess until more data is available. For example:
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L540 is found mostly in and around Germany and in Scandinavia. It would appear to be Germanic, but all L540 people descend from an ancestor who lived only 2000 years ago - too young to be part of the Germanic ethnogenesis. Additionally it appears to have expanded from Germany to Scandinavia rather than the other way round. So it could have been a lineage brought by the Corded Ware culture to Germany, which then became Celtic or Celto-Germanic until Germanic tribes expanded from Scandinavia to Germany. Only after that, during the Late Antiquity, did it start expanding from Germany, as what would be then be a Germanic lineage.
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CTS9320 has a distribution that could be compatible with a Hallstatt/La Tène Celtic dispersal. But it could also have been diffused by the Goths, if they picked up the lineage in Germany or Poland. The two aren't mutually exclusive. It could have originally spread with the Celts from Central Europe then, when the Goths reached Central Europe, they assimilated tribes with lots of E-V13 and brought more of that lineage across the Balkans. CTS9320 has a TMRCA of 3000 years, which places it right in the Hallstatt period. Its subclades expanded between 2500 and 3000 years ago, which corresponds to the Hallstatt and La Tène Celtic expansions. It's too bad there is almost no data at all from France, Belgium, Switzerland and Austria. Knowing what proportion of E-V13 in each country fits within which clade would go a long way to help us understand the origin of each clade.
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S2979 also expanded during the LBA and Iron Age. It is also found all over Europe, with the addition of Ukraine and Russia (including the Chuvash). The La Tène Celts did migrated to Ukraine and probably as far as the Volga-Ural region based on the presence of R1b-U152 (esp. L2) in the region, including high local frequencies among the Bashkirs. But the Goths also settled in Ukraine and
one of their branches almost certainly also found their way to the Volga-Ural. Once again, S2979 could have started as a Celtic lineage then have become Gothic in the Late Antiquity. That would mean that the Goths were a confederation of Germanic, Slavic and Celtic tribes, rather than a solely Germanic tribes.
Alternatively, S2979 could have started as a Corded Ware lineage (found in Russia, Ukraine, Lithuania, Sweden, Germany), then it could have become Baltic and Slavic in Eastern Europe, while other branches in Central Europe were absorbed by the Celts, Goths, etc.
I am still looking for a potentially Illyrian and Mycenaean branch, but without good data from Greece that is not going to be possible. At present the only two samples from Greece belong to the Y35953 and Z17264 (under CTS9320) clades. Not much can be said from only two samples in a country where 21% of the population belongs to E1b1b and most of it is E-V13.