Ok, but why afterwards ? Gaudo and Rinaldone (Remedello appear more autochthonous) are intrusive and different since their beginning from the Italian neolithic cultures. I agree that most of their population was local (EEF), but my guess is that the new brachy types that from the south reached the center of the peninsula were at least in part CHG. Mallegni described the brachy type of Gaudo as "Syrian looking" (unfortunately i have lost the PDF, it was a chapter of this book Dal bronzo al ferro. Sulla possibile origine anatolica degli etruschi).
I do agree with you that these Calcholitic newcomers could have been particularly enriched with Caucasus hunter-gatherer (CHG), but it's a mistake to associate Rinaldone and Gaudo only with these newcomers. Anyway there's too much at stake, let's proceed in an orderly fashion. We have during the Eneolithic/Copper Age/Chalcolithic Remedello culture in North Italy (Lombardy), Rinaldone culture in Central Italy (Northern Lazio) and Gaudo culture in South Italy (Campania). According to Grifoni Cremonesi Tuscany in the early Neolithic is part of the large Western cultural area, while the contributions from southern Italy and middle-Adriatic cultural areas are scarce. This is also true for Lazio.
La Toscana quindi, durante il Neolitico antico, fa parte di un’ampia area culturale decisamente rivolta verso occidente mentre scarsi sono gli apporti dalle aree culturali meridionali e medio-adriatiche.(...) Ben documentato è il momento successivo del neolitico, soprattutto nella Toscana settentrionale, con aspetti riferibili alla cultura di origine francese di Chassey e a quella della Lagozza dell’Italia settentrionale, che hanno un’ampia diffusione nell’Italia settentrionale e centrale.
The relations between the areas of Remedello and Rinaldone are very ancient, so that the copper for the ax of Otzi comes from the area where Rinaldone flourished, but It is equally true that from a certain point onwards Rinaldone had more contacts with Gaudo rather than with Remedello, and Gaudo was influenced by other southern Italian cultures like Laterza.
You lost the pdf, but fortunately I own the whole book "Dal bronzo al ferro. Sulla possibile origine anatolica". Some chapters are extremely questionable and quite airy-fairy, it's enough to read the first chapter where Chiarelli speaks about the Tuscan gorgia as an example of Etruscan legacy, just as only amateur scholars can do. Even children know that the gorgia in Tuscany is more widespread in the less typical Etruscan areas and less widespread in the more traditional Etruscan ones. How can be an Etruscan legacy? The Etruscan expansion in Tuscany started from northern Lazio and southern Tuscany, where the gorgia is non-existent. While other chapters are less vague and unrealistic, but the whole book is too much influenced by the publication of the 2004-2007 studies, and it is clearly obsolete with the conclusions of more recent studies, such as that of Ghirotto.
To begin with these intrusive CHG-like brachy newcomers aren't the Etruscans. Etruscan civilization flourishes two millennia later. At the most these newcomers are responsible for intensifying the relationship with the Balkans and any Aegean-Balkan-Anatolian connection.
These newcomers arrived from the southern Balkans and Epirus to South Italy, likely in an Apulian culture like Laterza, and from there to Gaudo and probably in the rest of southern Italy. From Gaudo they lately arrived to Central Italy.
If they are responsible for bringing an extra input of CHG, this extra CHG is still stronger today in Southern Italy than in rest of Italy. The distribution of this extra input of CHG follows the Italian cline, and Greeks have more CHG ancestry than the Italians.
Mallegni doesn't say that the brachy type of Gaudo are "Syrian looking", anthropologically it does not mean anything, he says that the cranial type and body structure of newcomers in Gaudo's culture remind the forms found also in Anatolia, Syria and Cyprus. And he describes them as high skull cramps, flat skull contours on the occiput, high body structure, robust body, well-developed musculature of the lower limbs (because they presumably walked long distances on foot). Mallegni is not describing a typical farmer, but the rading hordes of nomadic and belligerent warrior-shepherds with a superior copper technology that "who would have subjugated the local Neolitich population", adding that that they arrived in Italy from the other side of the Adriatic sea.
In a 1972 study, Mallegni analyzed some of Rinaldone's burials in central Italy (southern Tuscany and Lazio) and southern Italy (Gaudo in Campania). He argued that in the central Italian burials the average of these brachy newcomers was 15%, with 85% that were more typical dolichos EEF or mesaticephalic. While at Paestum, Gaudo's burials, the percentage of brachyphalic newcomers was 38%.
This 1972 study was resumed in recent times by Mallegni himself, in a book published in 2007. His conclusions seem more cautious, because new investigative techniques question the conclusions about the skeletal material analyzed in 1972. Ultimately, Mallegni says that the Tuscans burials are more similar to the rest of Eneolithic central-northern Italian burials and they don't have any resemblance with the Eneolithic Gaudo burials, if not very scarce. Mallegni adds that is currently thought that the Gaudo culture groups moved along the Italian peninsula reaching roughly the Lazio-Abruzzo territories. But those are sporadic presences and their presence is not strong like in the Campania territories. Perhaps their migrations to central Italy were stopped by the arrival of new populations during the Bronze Age. Are these new populations arrived in the Bronze Age the proto-Villanovians?
In conclusione si osserva che nel suo complesso il gruppo di Grotta San Giuseppe si inquadra abbastanza bene, per i dati metrici cranici, nella serie eneolitica dell’Italia centro-settentrionale; non presenta invece nessuna somiglianza con gli eneolitici del Gaudo, se non scarsissime. Attualmente si pensa che i gruppi a cultura Gaudo abbiano risalito l’Italia arrivando grossomodo nei territori laziali-abruzzesi. Vi sono presenze sporadiche e non la ricchezza della loro presenza dei territori campani. Forse l’arrivo durante l’Età del Bronzo di nuove popolazioni ha fermato questa loro tendenza. (...) Si può quindi concludere che verosimilmente i gruppi di Ponte San Pietro, della Valle della Fiora e di Grotta San Giuseppe appartenevano ad una stessa popolazione, che dalle aree costiere della Toscana e dell’alto Lazio si irradiò anche verso l’Arcipelago Toscano.
