Fire-Haired:
The Yemen Jews I have D-stats for are not very similar to Yemens. They're much more similar to Druze.
From what I can remember, Yemeni Jews are about 5% "African", all of it East African. The other Yemenis have much more "African", over 15%, I think, and roughly half of it is West African. The Druze, on the other hand, are about 1.5 % East African in the same kind of analyses. I think that's what moves the Yemeni Jews away from the other Yemenis, given the divergent nature of "African" alleles compared to Eurasian ones. That places them close to Palestinians, especially Gaza type Palestinians rather than the Druse, in my opinion, who have a lot more northern Near Eastern and even Iranian ancestry is their ethnogenesis stories are to be believed. The Druse, in turn, are closer to Cypriots. It's a mistake to think all "Southwest Asians" are the same genetically either now or in the past.
The differences show up very strongly in phenotype.
Druse:
It's not just pigmentation; it's head structure and facial structure and features.
Fire-Haired. Unless, SW Asians in 1000 BC had lots less African admixture or were somehow super EEF-like, both of which are unlikely.
How can it be unlikely given the known migration of entire Arabic tribes into the Middle East post the Islamic conquests? We're supposed to believe, according to Hellenthal and Busby and company that enough North Africans and Middle Easterners came into France in a forty year period (before being beaten back) to account for 20% of the total genome of Gaul, but whole tribes permanently settling in more northern areas of the Middle East didn't have any impact?
With those invasions came the Arab slave trade, where many East African women, in particular, were imported into the Near East.
I don't know how much of an impact they had, and neither does anybody else, but I do think this is part of what explains the difference in the results of isolated populations like the Druse versus Palestinians, for example, and in particular of Gaza type Palestinians and some Jordanians and certainly many Iraquis etc.
That's why using the Druze is a good idea, although maybe using the Samaritans is an even better idea, since there's no question of any outside genetic flow in them for the last 3000 or so years, absent the best idea, which is waiting for an ancient genome. Using Cypriots is not a good idea, in my opinion. We just can't assume that coastal Levantines were the same as modern Cypriots.
Oh, for what it's worth, I think the flow from the direction of the Arabian peninsula, which itself picked up progressively more SSA genes as time went on, was continuous at least since the time of the Nabataens. It just depends when you draw the line.