macOS Mojave on iMac won't boot into safe mode
I am relieved (and embarrassed) to report that the fault was a poor USB connection between the wired keyboard and the iMac USB port. A little unplugging and re-plugging solved everything. The iMac now boots correctly, in whatever mode I select.

The keyboard connection was only faulty in the computer's un-booted state. When booted, the computer accepted keyboard input from every key, including the various function keys.

The USB connections had been in place for about a year, since I bought the computer. Apparently prudence dictates that these connections be periodically unplugged and reconnected.