Automatically logged right back out of iCloud
My mac apparently won't let me log in to iCloud.
I am following the instructions (as per this guide Sign in with your Apple ID - Apple Support) but when I type in my Apple ID and subsequently my password, I (initially) get the two-factor authentication key on my phone, type that in as well. I can then see in my finder window than it connects and adds iCloud in the left hand side panel while the iCloud settings window is still churning. Then iCloud disappears from the locations list, the settings window stops turning it's wheel, and the iCloud settings window goes back to informing me of the many wonders of signing in to iCloud. Back to looking like the screenshot in the guide. No progress and back to square one. I am not logged in and can't access any of my iCloud services.
It's been a while since I was able to log in to iCloud on my mac. It's upgraded OSX (now MacOS) a few times and I have tried logging in to the Apple ID management site, removing my mac and starting the process over a few times with no luck. I am only getting the two-factor verification the first time after having completely removed the mac from my managed devices. After that, any subsequent attempts render the same outcome, but without the two-factor step. It seems that something in the process is not working correctly, that some part of the process has been completed and is registered as such, but that something goes wrong and I am not logged all the way out, but obviously also not logged in.
Can ANYbody shed some light on this phenomenon?
Having a macs, iPhones, iPads and AppleTVs seems a bit off, when I can't use iCloud. So please - any advice is warmly welcomed.
MacBook Air, macOS Mojave (10.14)