I still didn't know what the sound was, but I had decided that despite the high, birdlike tone, the metronome-like regularity of the call indicated that it was a mammal. By the time I got close to the source, I had narrowed it down to squirrel. A crying baby squirrel. The season was right.
Now you can see the dark nest in the deciduous tree to the right of the pine patch, with a green pine at its base. These photos taken after the fact. I hadn't seen the nest yet, when I was trying to home in on the strange peeping.