The stopper in the sink on Gretchen's side of the vanity can be lifted out, so it seemed possible that Julie had dropped the ring down the hole to see what happened. Or knocked it in there by accident, but the result would be the same. So last night, I emptied out the stash of assorted bottles and junk underneath her sink, grabbed a bucket, and removed the trap.
"Clink!" came the sound of something metallic falling into the bucket.
"Success!", I thought. I reached into the bucket and found that the small metallic object was the drain cover for the overflow drain in Gretchen's sink which had also recently vanished. So I put it back where it belonged.
The ring is still missing.
On the other hand, we did throw out a lot of bottles of no-longer-useful stuff that had been under the sink...