Please clarify whether the password prompt you're talking about is a popup window with a webpage asking you to sign in to your Google account.

The login that works in the browser, any browser, is the online login that comes up when you click the 'Gmail' button on the google search webpage. Have I answered your question?

No, you haven't. Let me provide further context.

You said both accounts are using the same SMTP settings, and you've removed and added the troubled account several times to no avail. If you are using the SMTP settings that the account wizard automatically applies, then you should be having OAuth2 as the Authentication method for the Gmail SMTP server. Is that the case? If so, then a window that looks like a browser window (but it's not a window of any of your installed browsers) should open asking you to sign in with your Google account. That window is Thunderbird's internal browser, and it loads the Google account sign in page with your account's username (email address) already filled. This window is part of the OAuth2 authentication method and at the end of that process, you are asked to allow Thunderbird to access your Gmail account.

I hope this explains it better, so confirm IF that window is the password prompt you're getting from Thunderbird. It should look like the first image posted here https://support.google.com/mail/thread/18092537/it-is-not-possible-to-add-a-new-account-in-mozilla-thunderbird-using-oauth2?hl=en (ignore the problem being discussed in that thread). If that's not the prompt you're getting, but instead are getting a prompt similar to this https://user-media-prod-cdn.itsre-sumo.mozilla.net/uploads/images/thumbnails/2015-06-06-02-01-01-cd736e.png then your Authentication method setting is not correct.

Thanks all OK now using OAuth2. It had re-installed itself after the account deletion with 'Normal Password. My 2nd account that worked was installed once only. Could it be that when I deleted the dodgy account that I should have shutdown Thunderbird before doing a re-install? As I did not shut it down, each install maybe picked up the SMTP that did not work. Thanks again for your help

None of the solutions mentioned above worked: The gmail popups won't let me enter passwords... it just refreshes over and over with the email account box.

The solution is in a Reddit post:https://www.reddit.com/r/Thunderbird/comments/v7ziud/how_i_fixed_oauth_problems_in_a_tb_profile_with_2/ step by step (I know and do NOT want to know anything about email; anyone here know how the US Postal Service functions?):

GO to Preferences -> Privacy and Security -> Web content

AND ACCEPT ALL cookies

it isn't clear if "accept third-party from visited" Keep until .... what the minimum settings for cooky acceptance and storage is. Need to fiddle with the settings but this INSTANTANEOUSLY allowed me to download ALL of my mail from three different accounts

Unfortunately none of the so-called experts here provided the correct answer and I wasted a full two hours

go to PREfence -> Privacy and Security Web content: ACCEPT ALL COOKIES

that did it for me, wasted full two hours going over and over above recommendations

go to PREfence -> Privacy and Security Web content: ACCEPT ALL COOKIES that did it for me, wasted full two hours going over and over above recommendations

You apparently did follow all the correct instructions for allowing cookies as advised in numerous questions. So no idea why you keep insisting it was such a problem. You are still not stating what OS you use which would be helpful.