In Chapter 9, Fausto-Sterling discusses the way in which psychological rewards "reinforce a behavior and repeated rewards intensify the behavior" (116). How does she incorporate the psychological system of rewards and punishments into an understanding of gendered color preferences? Could this same system apply to other gendered behaviors (e.g. sitting in certain ways, walking or talking in certain ways, pursuing gender-appropriate pastimes)?
You don't mention a book here, but I assume you mean the book Sex/Gender: Biology in a Social World. This is a fabulous question to think about, especially if one is a parent (like I am). Chapter nine is amazing. In this chapter, Fausto-Sterling shows us that reinforcement of "a behavior and repeated rewards" can also determine gender color preferences: girls like pink, boys like blue.
The quotation you provide is an important one in understanding gender color preference because parental behavior serves to "reinforce a behavior and repeated rewards intensify the behavior." In this sense, you almost answer your own question! Fausto-Sterling simply expands more upon what these "repeated rewards" can be. Due to her description, we can understand these rewards. For example, a little girl can be dressed all in pink lace and the parent would say, "Oh! You look like a little princess! How BEAUTIFUL!" Or, without asking the child, a birthday party can be planned with a "ribbons and bows" theme, again, all in pink. When the child opens her gifts, the parent can show excitement about gifts such as baby dolls, dresses, and such; however, that same parent could simply show neutral (or even negative) reinforcement if something like a toy car is given.
The same psychological system could be used if the child is a male. We simply reverse the process. For example, a little boy can be dressed all in blue with trucks and trains all over his clothes and the parent could say, "Oh! You look so handsome!" Or, without asking the child, a birthday party could be planned with a "cars" or "trains" or "planes" theme, again, all in blue. When the child opens his gifts, the parent can show excitement about gifts such as model trains, matchbox cars, etc.; however, that same parent could simply show neutral (or even negative) reinforcement if something like a doll is given.
In conclusion (and in answer to your second question), yes, this same system could apply to other gendered behaviors as the author explains in Sex/Gender: Biology in a Social World. In this sense, Fausto-Sterling mentions mostly negative reinforcement. In regard to a way of walking, I can just HEAR a very traditional parent saying, "Billy! Don't walk like that! You look like a girl!" or "Susan! Hold that fork properly! You are eating like a farmer!" or "John! WHY would you want your hair that long? You look like a GIRL!" or "Alice! A pixie cut?!? You look like a BOY!" This, of course, could apply to absolutely any behavior stereotyped to either gender.