At last I figured out that it worked when I clicked it quickly, and not when I did it slowly.
Ran xev, saw that it wasn't generating mousedown or mouseup events if I did a slow click-and-hold-and-release, but it did generate both of them --- at the time of mouseup --- if I did it fast.
Hunting around on the internet eventually revealed there was some sort of scroll wheel emulation turned on by default, whereby you can click and hold the middle button and meanwhile move the trackpoint and get scrollwheel behavior.
