I found once my kids had one sign down pat, they tended to use it for everything for a while. Almost as if they know to use their hands to say something, but they only knew that one word. Tallon signed book for everything and Kayla did milk.

I think if you think it's a mindless sign, just ask her if she's wanting milk, repeating it to her.. just to reinforce that what she's doing means milk. In the book I was using it said not to rush and do everything just coz they signed it. You can still say no if you think she doesn't need milk right away. But you can still teach her that what she's signing means milk. If that makes sense

Maybe it's time to introduce a few more signs. I found my kids started pointing at things as if asking for the sign. But yeah, they did tend to use their first sign for everything for a while.