Well, I agree with what you said, partially, in that,
"The Israelis today claim to be Ashkenazis and the chosen people of God. But their own Torah (Old Testament) says they are "gentiles" in those aforementioned verses
You mind talking more about our journeys into the Caucasus?
. I'm trying to draw a timeline to understand this better."
Pioneers definition of CAUCASIAN absolutely fits today's world, but it is also completely admitted by scholars today, in that the term for White Europeans in these modern times as being CAUCASIAN stems from a movement. This term revolves around 'a racial construct', from what I can see but this term originally did not apply to White people. I think one of the best examples in this movement may from my research might be understood with a comparison to another term.
What do you think about or imagine when you hear the term to refer to SOUTH AFRICANS?
Today, we know that this term CAN apply to White Europeans who have been a part of South African for many decades since the Colonial times, however, the ORIGINAL SOUTH AFRICANS still exist in South Africa amongst these White 'SOUTH AFRICANS'. The origins of the White 'SOUTH AFRICANS' does NOT directly stem from all of the White Europeans intermixing 'sexually' with these Africans, but they migrated down into South Africa and dominated over the original South Africans. This modern RACIAL CONSTRUCT OF TODAY'S 'SOUTH AFRICANS' [White] would absolutely not define their origins as steming directly from sexual selection with the Black indigenous South Africans who also came to be in South Africa at a much earlier time.
So, the origins of the ORIGINAL CAUCASIANS becomes relative to a certain time period in how they came to exist and then yes, intermix with White people who now are called CAUCASIANS. But as PIoneer did reply, he does not really believe this process in the way that I have explained it, however, he does contradict himself, IMO, but he won't admit it.