Paddy, I do use a different 11-13 digit password for each time I need one (dozens!). I have a unique way of remembering them. I will look up how to use a password manager.
However, that still does not solve my original question. I did change my iCloud password as Xairbusdriver suggested, but...
1. When I reboot my old iMac, the iCloud window shows up and asks for the password. It does NOT accept the password that works on the other devices. I then click CANCEL twice and that window goes away. Problem solved? I don't think so.
2. Another problem, related to this or not, is that not all my 17,500 photos on iCloud are present in Photos on my iMac. No photos are visible here after Dec 2019.
At the bottom of Photos window, it states "17,500 photos. Uploading 13,900 items". That uploading number hasn't changed for weeks. No idea if it's uploading or stalled. Are those the missing photos?
Any suggestions here? Thanks again, TS!
Aside, I do want to transfer all files to my new 27" iMac, but I want all glitches I have had for a while in Photos, Fonts, iCloud cleaned up before I do that. Trying to fix one glitch at a time now.