I think I’ve got it placed now, although the answer doesn’t make a lot of sense to me. Remember the Equipoised “Purse” and “Clasp” pencils?
That’s ten out of the eleven known colors -- or maybe eleven out of the twelve (see http://leadheadpencils.blogspot.com/2015/02/only-eleven.html). The “purse” pencils, the five on the left in this picture, were in “girlier” colors and had a single, deco-decorated band. The “clasp” pencils, on the left, were found in “maniler” colors and were distinguished by a pair of plain, thinner bands. I think the clasp pencils are the nearest relatives to this one:
Note that there’s just one difference: on the ringtop, the break between cap and lower barrel falls below the bands, while the clasp pencils break in between the bands. So I guess this was supposed to be the ladies’ version of the manly part in the least manly line?
Speaking of purse and clasp pencils, I've got a nice set to show you as well:
The color on this NOS set is superb, and the only thing more I could ask for would be the lid for the box. I fished around on Facebook and heard that the lid was cardboard, and if I see one, I’ll post a picture of it.
This is that mysterious color, which may or may not be what was called “Ceylon Pearl” in Eversharp’s 1932 catalog. The catalog shows Ceylon Pearl, but the color is more of a greyish/pinkish hue than what you see here. Unless the colors were wildly off in the catalog, this is an unnamed twelfth color.