I thought I'd go ahead and post here, which would mean less needless trouble for other general readers of this particular forum.
Here's the history. I built a dual-boot Win7/win10 system, creating two different OS-system volumes on the same disk. I was able to install NVMe drivers for Win 7 and then clone the dual-boot SATA drive to NVMe. Then, we had the Creators 1703 build, and I went through a couple weeks' trouble restoring the dual-boot functionality. No problems since. Win 10 Fall Creators 1709 is currently deferred for a year, while allowing "non-feature" updates. But today I encountered a problem with Win 7 Updates.
I may eventually remove Win 7. I believe I missed about two months of the monthly rollup package in Windows Update. So after those two months, I decided to boot into Win 7 and do any "maintenance."
I find Windows Update was broken. It tells me the service isn't running, but "Services" tells me that it is -- indeed -- running.
So . . . I came back here to see more recent posts. I had gone through all the misery people experienced between 2015 and 2016, but there'd been no problem after that until now.
I also did a more general search of "How to fix Windows Update problems in Windows 7," and HowToGeek popped up in the list.
Apparently, some tweaks had been made in Windows 7 so there's a link under "Troubleshooting" to "fix Windows Update." I ran it. Suddenly, the missing update "History" (symptomatically missing under these circumstances) was restored, 9 new updates detected, downloaded and installed.
Ho Hum. This still leaves one with a mild sense of discomfort. But -- I'm mostly using Windows 10.
[written, submitted under a Win 7 boot session and happity-joy . . .]