iMac running on external SSD won't boot from it after upgrade to Catalina
UPDATE
I found that I can boot from my external SSD reliably as long as my external HDD for Time Machine is not connected. No need for the extensive process below - just power down, unplug external HDD, and my Mac can boot from the external SSD.
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I had the same issue and neither the SMC reset mentioned here or the NVRAM reset discussed here worked.
But the workaround I found to reliably boot off the SSD is:

Power off the computer
Disconnect the external SSD
Power on the computer (which will boot off the internal hard drive's OS)
Connect the external SSD
Login and shut down
Power on while holding the option key
Select the external ssd from the menu and the computer will boot off the SSD