Any black other than the tail is not desirable, and if you were showing, it does count off for judging a Buckeye.
So, the second picture is the other pullet?
Also, you are not looking for brown or shades of brown really but RED. Some Buckeyes I have seen do look more brown than red, which is not what you should be looking for in the breed. The SOP calls it a "rich, mahogany bay". Of course, the term 'rich' is subjective, and not everyone agrees on what exactly the shade of color should be, however, darker is better if you can get it without getting black popping out like your pullet in question. I find that my darkest birds have this, especially this year's crop. Ideally, you want a nice even color from head to tail, but I also see a good number coming up with black in the neck that mostly is covered by the time they reach maturity. But all the talk about color is mute if you don't have a good bird as far at type. I wouldn't get rid of a pullet who has a couple black tips if she had very good type and had a male to breed with that might clean up the color. Now, if you breed her with a male who has black showing, your next generation will likely have even more than the parents, or at least a good number of them. Try to breed to a male who has good, clean color and not orangey colored.
Regarding color, if you read some of the history of the breed, Nettie Metcalf stated that the color should be 'so dark as to appear black from a distance'. I have yet to see a Buckeye that dark. That isn't exactly what today's SOP is looking for either, in my opinion. Like I said, the SOP description is somewhat subjective. Now, if I had what I would consider a light colored pullet, she would go find a home where she can lay eggs and not breed. Same goes with any fluffy Buckeyes, the feathering should remain somewhat tight to the body, just not as tight as a Cornish or other Game.