I have a 21.5-inch, Late 2013, 2.7 GHz Intel Core i5 iMac
On the built-in SATA Hard-drive I have High Sierra OSX installed - I retain it because I have several applications which don't run on anything more recent.
I have an external SSD with Catalina OSX attached via USB which is my boot drive for everyday purposes. (also this SSD is divided and has Mojave as well)
Everything was running fine until recently - I could reboot, hold down the OPTION key and select which disk to boot up in.
But now when I restart (from the Apple menu) and hold down the OPTION key it only shows the internal HDD - no SSD nor Time Machine Drives (SATA connected via USB). I have to press the Power button and physically restart, and then hold down the OPTION key - only then does it gives me the full range of bootable drives.
Selecting which startup disk in the system panel isnt the issue. It seems to be something to do with it not recognising external drives (even time machine ones) from the Menu Restart.
I've tried resetting PRAM, also left it unplugged for a time. No joy.
My only other piece of info is that this seemed to start when I was updating Catalina - always a bit of a pain when located on an external disk. I wonder if there is something left unfinished - but that might be a red herring.
I unplugged all my drives/peripherals and reset SMC and NVRAM. As I plugged each back in one at a time and restarted - it seems that one of the external drives is causing the problem.
It has no OSX on it, but it seems to prevent the SSD from being recognised without going into a power off/on restart.