The mystery has been solved! Elizabeth Alles wrote me recently to say she'd found the source: an altarpiece of the Adoration of the Magi, by Stefan Lochner, in the cathedral in Köln (Cologne, Germany).
Sure enough, there is my Mystery Lady, in the left wing of the open altarpiece, over there at the far left margin:
The best closeup view I can get from the online images is this:
There are two particularly interesting things about the beads in this painting. One, here's another instance of red coral beads with (this time) especially clearly painted gauds of clear, colorless rock crystal. I'm keeping track of instances of this combination, because it seems to be a favorite attribute of saints and holy people in paintings.
Also, here's a straight string of Christian prayer beads -- not a closed loop -- being carried by a woman. While I've seen women with this type of beads before, it's not at all common: generally women have loops and the straight strings belong to men. But not always, as this painting shows!
According to the Web Gallery of Art, this altarpiece was painted in the 1440s, not for the Cathedral (where it is now) but for the town council's chapel in City Hall. Though it doesn't look particularly large in the photos, it's huge -- more than 8 feet tall (260 cm). This explains why it's painted in sufficient detail that a small snippet of it, like the "mystery hands" bit above, is clear enough to use as the cover of a book. (This is on the cover of one of my main reference books, 500 Jahre Rosenkranz: 1475-1975.)
Not a lot is known about the life and work of Stefan Lochner, the painter. He was born in Meersburg am Bodensee in about 1400, and died in Köln in 1451, probably of the plague. There's considerably more information about him and about this painting in the notes from a University of Wisconsin art history course taught by Prof. Jane C. Hutchison a few years ago, available online here. A lot of his paintings are still in Cologne.
As for identifying the people in the painting, both wings of the altarpiece seem to show saints and holy people witnessing the central scene. Interestingly, only one figure on each side seems to have a halo. Why?
On the left, the haloed figure is almost certainly Saint Ursula, since she has that saint's attributes of a royal crown (Ursula was supposedly a princess) and an arrow (by which she and her companions were martyred). So it's likely that all the other women in the front rows of the crowd, including the lady with the beads, represent some of Saint Ursula's eleven thousand companions.
There are other people in the back who clearly have some other identity, since we can see their hats: there's a bishop's miter, and next to him a rather beehive-shaped hat worn by someone carrying a staff topped with a cross. I'd think that was a Pope, except that his hat doesn't have three rows of crown-leaves on it as the Pope's hat classically does. (Dr. Hutchison suggests some identities in her article.)
Ursula is specifically one of the patron saints of Köln, since that's supposed to be where she and her companions were martyred. That might explain why she's the only one wearing a halo in this picture. The others might be holy people too, but she is clearly special.
Logic would then suggest that the haloed man on the other wing of the triptych might be a special male patron of Köln. And sure enough, there is one: Saint Gereon (d. ca. 304), a Roman soldier, martyred with 290 others on order of the emperor Maximian for refusing to sacrifice to pagan gods to obtain victory in battle. (He's also the patron of people with headaches and migraines, a useful saint to know.) The figure in the triptych is certainly similar to other 15th-century German ideas of what a Roman soldier looked like: in fact, when I went to the saints index here, the image of Gereon is almost, but not quite, identical. The caption there says it's another image from a Köln painting (now in the Wallraf-Richartz Museum), this one by an unknown painter in about 1480.
There's a pleasing symmetry to the wings of this altarpiece, Ursula with her many companions on one side and Gereon with the rest of his regiment on the other.
I did scan the painting for other interesting rosary beads, but didn't see any offhand. I always look, because if one figure is carrying them, sometimes others will too.