How do I create an app-specific password for iCloud?
The missing information was provided by @GordonDavisson (and if he wants to post an answer I will accept his instead of mine):


  To generate and use app-specific passwords, your Apple ID must be protected with two-factor authentication.


This is actually on the Apple Help page, but oddly not included in the section "How to generate an app-specific password" (even though it was the missing step for exactly that question) but instead buried between an explanation of what an app-specific password is (which was of no value to me) and fine print about different OS versions.   I used the headers to skip right to the relevant information (which is what headers are generally for) and didn't guess that a critical piece of information would be placed elsewhere.