I took her in to Dr. Walton this morning, and his diagnosis is detached retinas, caused by age--she's almost 17. Maybe some genetic predisposition, but not some other health issue. (I'd spent a restless night thinking "brain tumor".) In her case, he said, the lenses have broken loose and migrated to the back of the eye, again probably because they shrank with age, and that probably triggered the retina detachments by changing the pressure on the fluid in the back of the eye. Or something like that. Googling seems to always attribute detached retinas to hypertension and says that should be treated immediately. I have a call in to the vet... [Note from later--he didn't call back, so the question will be asked of Dr. Dunn tomorrow.]
Which brings up another reason why I delayed some on this, plus some other less critical problems Agatha has. I dislike Walton, and the vet that I do like, Dr. Dunn, has left Walton's practice to go to a Pets Are People, Too--one of those Evil Mega-Corporation places that's buying up lots of independents. And the office Dunn has gone to is 20 minutes or so away, where Walton's office is 2 minutes. Distance is important when you have a cat who finds all carriers and car trips traumatizing. This morning I first tried to see Dunn, but she was not in today. Made an appointment for tomorrow, anyway, and went ahead with the emergency visit to Walton. If the drive isn't too much for Agatha, and if this other office setup seems OK, I will probably keep going to Dr. Dunn for Agatha.