For the past couple days, once I've turned off my Magic Mouse and put the system to sleep as usual (via short touch of power button) over night, the system shuts down completely — with no log or error message indicating why. DU indicates that nothing has gone awry.

Is this an omen of impending iMac failure? Or what?

Running El Capitan 10.11.6 on mid-2011 iMac 2.5 GHz Intel Core i5.

Sounds like you may need to reset SMC. Read How to reset the System Management Controller (SMC) on your Mac

Are you certain you aren't holding the power button a touch too long and thereby triggering a shut down?

See what happens if you first switch off your mouse, then sleep your Mac with the keyboard: CMD+ALT+eject key

Taking a different tack, I'll wonder if, perhaps, your power button has deteriorated after years of use?

jon & joemikeb & freelance & artie: Many thanks.

No change in my short touch of power button, but since the following suggestion helped I think I'll just keep resetting the SMC in reserve.

The sleep keystroke combo (option-⌘-⏏) seems to do the job.

So, rather than tempting fate, I think I'll switch to that (for putting the iMac to sleep after turning off the Magic Mouse) and leave the power button alone except for booting.

Why not just take the path of least resistance and use  > Sleep?

With the Magic Mouse turned off, one can't access the drop down menu (as far as I know).
And if I do that with the MM turned on and then turn it off, it causes the iMac to wake up.

Sorry, I've got no experience with the Magic Mouse, so I thought you could save the "turn it off" step. I guess you turn it off for battery conservation?

Glad that worked for you.

I'm curious to know where you find those keystroke icons?

Resetting SMC is very easy and has no adverse effects. I have done it with my iMac, and all it involves is shutting down completely, unplugging the iMac for a short time, and plugging it in again. If you have a power outage, the effect is the same.

And right on point:

They are all over the place and often not easy to get to. In virtually all versions of MacOS  is achieved by Shift+Option+K (⇧⌥K). In Mojave and Catalina the rest can be found somewhere in Emoji & Symbols (∧⌘space). NOTE: Emoji & Symbols has two UIs. The default looks like this and you can find some of the symbols browsing here. However if you click where indicted you will get this view. For reasons known only to a few developers there are symbol sets available in the second view that do not appear in the first, specifically "Technical Symbols" which is what you are likely looking for. No the apple logo does not appear in either variety of emoji and symbols or at least I have never found it, but it is available on the keyboard as ⇧⌥K.

Thanks for pointing out the other view (Surely, they could have hidden it better! ); I knew there was stuff missing.

I've got  from somewhere - The only place I can think of is an ooold symbols viewer...back in the days when it showed the entire Unicode sequence. - but it shows up in my favorites like so...whatever on Earth "PRIVATE USE AREA-F8FF" is.

More:

⌥⌘+⏏︎

Thanks!

I can't claim any genius in finding that. It was purely curiosity that caused me to check what that little icon up there at the right corner of the Character Viewer window did and voilá I struck gold. Instead of hiding it they could have shown the Technical Symbols in both views but perhaps with a warning that "Symbols on this page are not Unicode standard." My aggravation is I have not found a way to add symbols from the small view to the "Favorites list" in the default view 🤬. Nor have I found a way to add  to the Favorites list 🤬🤬

Time to submit another suggestion.

I've got  in my Favorites list; I assume it's been there since the days when the Character Viewer displayed the entire Unicode sequence.

I'll be happy to send you the file if you can figure out where it lives.

I"m not sure why I never clicked on that icon, but then again, it took me a few years to learn to look for answers to questions by cruising the menu bar.

More: On second thought, isn't the key command much easier to use than the Emoji & Symbols pane?