kevin wrote:
After a little more digging, I think I have your answer (and mine too).
Google for "Surfactant Leaching"

Although the picture on all of the pages is rather extreme, the
description and conditions match our scenarios almost exactly. A rare
condition, and apparently almost always with newly applied paint, and
relating to humidty and moisture.

You obviously had moisture problems. My closet gets very humid, because
it is unheated and in a far part of the house.

Hey, Kevin, thanks! I did Google "red mold" before I made the OP; none
of the search results mentioned this technical term (surfactant
leaching).

Now this kind of stuff is what makes me like the Internet. (Just had
my identity stolen for mucho dollars, and that kind of stuff makes me
hate it.)