What prevents you from setting up the second Gmail account? You'll need to be more specific about your problem.

Just running the new account wizard and fill in your credentials should do. https://support.mozilla.org/kb/automatic-account-configuration

Many thanks for your reply. I don't get the account setup wizard, my first gmail account was set up long ago, so I tried ' add a new email account (using File > New > Existing Mail Account… or via the Account Settings). From the menu on the right of my T Bird screen I click File and it produces 'get new message for.., subscribe, compact.., and offline. Account Settings shows all the settings for my existing account, so I tried editing them with the details of the address I want to add. No joy there either. Clearly I am stupidly misreading something and I'm sure that there is a simple solution but I'm not tech savvy enough to see it.

From the menu on the right of my T Bird screen I click File

I don't know what that means.

I'd suggest you re-read the instructions in the article linked above, and follow them: File > New > Existing Mail Account

I click File and it produces 'get new message for.., subscribe, compact.., and offline.

You're supposed to click File > New > Existing Mail Account

Note, 'Existing Mail Account' here means an account you do have with an email provider, but not yet set up in Thunderbird.

Account Settings shows all the settings for my existing account, so I tried editing them with the details of the address I want to add.

You're not supposed to edit an existing account. 'Existing account' here means an account already set up in Thunderbird.

You're supposed to click File > New > Existing Mail Account

Thanks christ1, I must have been trying your patience. I was looking in the wrong place for File>New etc. Now I have a new problem: Google is blocking my sign-in because 'Someone just used your password to try to sign in to your account from a non-Google app.' I'll log in to Google and try to solve it with them. Thanks again

'Someone just used your password to try to sign in to your account from a non-Google app.'

You'd get this kind of warning when connecting to your Google account using Thunderbird with OAuth2 authentication the very first time. Google require you to give permission to Thunderbird to connect to the account. This is how it works. Typically this process doesn't block the Google account. So you'll indeed have to check with Google what's going on.

Thanks again.I've sorted it out with Google at last!