macOS Mojave on iMac won't boot into safe mode My iMac (late 2015, 8/1TBSSD) has run happily for more than a year on High Sierra, and I just now upgraded the OS to Mojave. Now, the machine won't boot into safe mode or into Recovery. When I hold down the appropriate keys before or at the startup chimes, the regular boot ensues. Booting is brisk and correct. No firmware password is set. The keyboard is a wired Apple keyboard A1243; in use it gives no indication of fault with any of its keys.

In all other respects, the Mac operates as it should. I updated my MacBook Air (mid-2013, 4/512SSD) at the same time using the same Mojave installer, and the Air behaves as it should. 

What's gone awry here, and how might I return the iMac to its correct functioning?
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.