I'm not quite sure I understand what you mean by breaking down this unity of the "caucasian" element in northern Italy. That element is clinal in Italy, like virtually everything else; caucasus is 22.8 in northern Italy, about 28 in Tuscany and 36 or so in the south on this calculator.
Within the north, the academic sample from Bergamo and the more general north Italian dodecad population have virtually the same amount of 'caucasus' component.
The interesting thing, as I've mentioned before, is that Oetzi's caucasus component on the same calculator was also 22%, but Gok 4, also a Neolithic farmer, only had about 5%. So, does the caucasus component in Europe represent a later and slightly different Neolithic migration, and/or is this a sign of the beginning of the metal age migrations. After all, not only did Oetzi possess copper tools, but he had high arsenic levels in his blood, which indicate he probably was a copper worker, and let's not forget that metal working first moved from the east into the Balkans, and then later came east again with other migrations.
As to the relationship between the Gedrosia and West Asian components, this is what Dienekes has to say about it:
"Similarly, the West_Asian component (from K=7) is intermediate between the Caucasus and Gedrosia components; the Gedrosia component diverges in the direction of the Asian groups (not shown in this figure), and in particular of South Asians.
Caucasus/West_Asian components are definitely not comparable across calculators, since 'dv3' used a "West European" category that the other calculators do not, and which was shifted toward West Asia relative to the other "East_European" component."
As to the K=12 versus K=12b calculators, this is what he has to say: "The additional step of distant relative filtering may also have influenced overall component levels in some cases. Its overall effect is to preclude the creation of population-specific components. Such filtering did take place during 'dv3' for populations with known sets of apparently distantly related individuals (such as the HGDP Arab groups), but it was done with a uniform procedure across all populations in K12a/b."
Different calculators were done at different times, and the later ones are going to both include more populations and be more refined that the earlier ones. Also, some calculators were created for specific purposes, such as the Globe 13, which was meant to clarify the issue of the SSA component in West Eurasians.
His best explanation of the relationship between the Caucasus and West Asian components is here in his discussion discussion of K=7b versus K=12b:
http://dienekes.blogspot.com/2012/09/inter-relationships-between-dodecad-k7b.html
Gedrosia is just Caucasus with a slice of South Asian. Perhaps a population from further south toward South Asia that picked up a lot of Caucasus during their stay in that area. When the Gedrosia component is not included, I think this is where the South Asian that people get comes from...