Login using an ext drive

Yes it takes 1-5 days or usually 2 -3.

It is old but works fine after it manages to load. Late 2012 running updated Catalina installed on an external HD

Seagate backup plus slim 2TB. Catalina is the last version it will accept.

Every update usually requires a restart. I hold the Option key down for

60-120 seconds immediately after the startup sound is heard. I can hear the Seagate start and run. Usually, it stops while the Option key is still depressed. Cannot figure out the exact pattern to follow. It runs white for a while, maybe Apple shows and starts loading, then goes black or grey (showing only modem and country in the top right-hand corner), maybe comes back to Apple, says it will be 28 more minutes, etc etc. It eventually shows up with the login screen.

It may take longer than usual partly because it starts on an external HD, plugged into a (non-thunderbolt) USB slow-speed, and because I have the worst internet speed of only 10Mbs. If I can ever get better internet speed, I will buy a new iMac. I may do that anyway.

Some have suggested going to Preferences and set Startup disk to external HD. I am familiar with that, but do I click "Target Disk Mode" thereby setting it to always use ext HD to start? That was not clear to me.