To me, this is a poem about what women have traditionally been compelled to do for men -- how they have been pushed to make themselves into what men want and how this forces them to submerge their true selves.
In this poem, the author is trying to see into the mind of the woman in Utamaro's print from 1700s Japan. She notes how the woman is making herself into something of beauty (notice how meticulously Song describes the room and how she then segues directly into describing the woman as if the woman were part of the beauty of the room) for someone else's pleasure ("some other hand will trace"). She then tries to uncover the woman's thoughts, but it seems as if the woman has none. The woman seems to want to be something other than her beauty, but ultimately she does not speak or think anything.
This shows that the woman has truly submerged herself. She does not allow herself (is not allowed by her society?) to be anything but a beauty, made for the pleasure of others.