Thx Tom. Upon further review, I noticed that it was actually when pressing the brake that the light came on. On further further review I noticed one of the still-working brake bulbs was kind of old (filament looked worn, inside glass somewhat blackened). Replaced. Dash indicator out. Moral for posterity: even a working light that's old can throw a false failure reading. So for this problem, I had both a failed high-mount stop, and a failing rear brake light.
Fixed.