Wouldn't it be that the person in very foggy location would be lighter, since the fog would block much of the light? Of course it depends on the distance from the equator for each person.
So temperature doesn't matter, just light level, am I correct? (ignoring vitamin D in the diet)
I said 300,000 to be absolutely sure that the change would occur in time, though that would probably result in the evolution of a whole new subspecies. Also, it takes less than 10,000 years if there are already many different skin tone genes in the population, while it can take many more if they aren't. For example, there are no black native Americans. And they crossed 17,000 years ago. Even if it took a full 7,000 years to arrive at the equator, they'd still have the alleged 10,000 years. Even the natives that had almost the full 17,000 years, those in Canada, are, according to their latitude, not yet adapted.