Amazon typically only ranks one color variation per keyword. Some niches are the exception, but we've found one variation to be the most common. This means you need to choose a specific color variation to target (NOT the parent).
Let's say your product is a dog leash and you have 3 colors (red, blue, yellow) and 3 sizes of each color (small, medium, large).
The 'red" dog leash might be ranking for the keyword "dog leash". If so, the "blue" or "yellow" dog leash would typically not show up in search for "dog leash".
Now, the different sales of the sizes of the "red" dog leash all attribute to the keyword rankings for the "red" dog leash.
Simply put, regardless of sizes, Amazon has determined through sales and their own relevancy that the "red" dog leash is the most relevant color variation out of your listing for that keyword.
If a variation is already ranking for your desired keyword, that is the ASIN you need to target. If you don’t have a variation ranking at all for a keyword yet, then choose the one your research has lead you to believe will be the most popular.
NOTE: In our experience, it has been incredibly hard for Amazon's system to switch a color variation in regards to a ranking keyword. We did some testing with a few of our brands in the past and it worked 50% of the time.
Typically, Amazon gives keyword ranking to the variation that is selling the most if a particular keyword. I say typically lightly and I have seen quite the opposite in some cases.
Some people have had success "forcing" a switch by running a large sustained promotion. It depends on what the variations are already selling too. We would not recommend trying to force a switch with a large promotions due to the varying results we have seen in the past.