Additional information: the Google sign in page comes up but when I click "next", nothing happens. I just added the same email account in Apple Mail on the same computer without any problem so this is clearly a Thunderbird issue.

I don't recognize that Google log in page. Maybe something has changed at Google recently. Did you enable OAuth2?

Do your two Gmail accounts have distinctive names? I usually set the name of an account to be its email address, which is almost certainly unique. The default account name might be just the provider's name, and two accounts with the same name may well be the cause of the "server already exists" message.

Zenos, there are at least two other users getting that same screen. I have never seen it before and I am not sure what it is.

OAuth2 is automatically enabled. I have three gmail accounts and they each have a distinctive names. The "server already exists" error message goes away if I restart Thunderbird. but Thunderbird doesn't quit properly, I have to force quit. These two things suggest there is a process going on in the background. As I said, I set this account up on another computer with no problem.

Another update: I just got Security Alert from Google saying that there has been an attempt to access my email account from an insecure app and that it was blocked. Sounds like Google doesn't recognize Thunderbird as a secure or is there some setting that I need to change on my Thunderbird set up?

Okay, I did a complete shut down and restart and now it works! The Google sign in page was different this time....allowed me to add my password. Thanks for your help.

The OAuth2 setting should avoid the "insecure app" messages....but the specific mention of Thunderbird in the Gmail message suggests they have set something up to detect the mail client in use.