Thank you, @RayofLight62 and @Letitia. I guess that French guy was right. Haven't tested the fix yet, but I am confident it will work. And I'll get the click rhythm down soon enough.
I spoke too soon. The first time I had to change the battery, everything started up just fine afterward, but this round I've tried five or six times with no success. I pop in the battery, "SX Mini" shows up on the screen for a few seconds, the screen goes dark, and when I nudge the joystick upward twice nothing happens. Bah humbug.
I've put the Pico back into service till my anger at the SX Mini fades. Right now, I'm so irritated that I'm afraid I'll cross-thread the battery cap (whose coarse threading I've come to loathe) as I impatiently try again and again to get this thing to work.
Do you think I'd have better luck with a 20700 or 21700?