I would have said that you just enter your username in the space provided (your apple id)

Then click retest. An I missing something obvious?

Well, the answer is not obvious. There doesn't seem to be away that entering actual values will hack it. I shall delve around in my Apple account and there support, and see if there is an answer there. If I can figure out what to do, I shall come back here.

Apple offer this page for getting email settings: https://support.apple.com/en-gb/mail

However I cannot make them work. I give up. I hardly ever use the icloud.com account - and can readily monitor them on my Apple devices, or on the web.

I could change my apple ID to the icloud one - but not for now.

Well, the answer is not obvious. There doesn't seem to be away that entering actual values will hack it. I shall delve around in my Apple account and there support, and see if there is an answer there. If I can figure out what to do, I shall come back here.

Your issue you said was there is nowhere to enter your non apple appleid. That is the username field in the image I posted. You enter the icloud email address when first asked for your account setup and your appleID as it is your username in the relevant box and click retest.

If that does not work, disable any antivirus products because they are good at messing up the whole account creation process. Norton's for instance decides you are hacking the server and completely blocks access.

I switched to an icloud.com email as my Apple ID, but that didn't solve the problem either.

Finally, I found that I had to set up an app-specific password via my Apple-ID page - see this explanation: https://www.reallinuxuser.com/how-to-set-up-your-icloud-email-account-in-thunderbird/

It's written by a Linux user - but it worked fine for me too.

Posted here in case someone else in the future is struggling like I did.