When seperating out each trait such as red heads, your explanations make more sense, but people of different race arent just defined by one characteristic. Its a whole assortment of things. Take albino africans for example. They have white skin, but there is no mistaken what race they are. Those traits dont change until you introduce a new race. Why is that?
Red heads should be there own race btw.
Like I said in my previous posts, there is no reason for the grouping of those characteristics into one "race".
Here's a fairly typical Italian (white):
or
Why is that phenotype closer to this Irish (white) one:
Than to this Algerian (not white) one:
Now I am sure you can find some average difference that are closer in one group than another to make a point about some characteristic litmus test, but the decision is arbitrary.
Race exists because as Europeans developed closer ties under Christianity and set forth to explore the world, they found non-Europeans who had different looks and cultures. So they designated themselves as "white" based on their average skin color, to differentiate themselves from the "others".
If no such historical fusion happened, something else might have come along. Maybe Islam would have united the Northern Africans with the Spaniards, and they set forth as the Tans to differentiate themselves from the other "races".