Thanks for all the replies!

I got the light used, with no documentation; I have emailed the good people at Planet Bike and have little doubt they'll send me a pdf at some point, but nothing yet. They have pdf's of some manuals on their website, but not this one.

You're quite right, there is a steady mode and a flashing mode. I think I knew that at some point but had forgotten it. Evidently that's part of the problem, but not the whole problem.

Playing with the light late yesterday afternoon, I determined that the switch (which is a mechanical push button) has three settings (off, steady, and flashing) and each push of the button clicks it to the next setting, after which the cycle repeats. Okay. But sometimes the 'steady' function doesn't work; and sometimes the 'steady' function works for a short while and then cuts out. After this happens, the 'flashing' function still works, but doesn't seem to work quite right. Then, after a while, everything goes back to normal, all settings work correctly. For a while. And then it starts misbehaving again. So I remain as puzzled as before.