dual (two factor-auth) gmail accounts in Mail.app
You shouldn't use your Google account password to sign in to a mail app. Instead, use an App Password. That's because most mail apps can't handle a two-factor auth code. For more information, visit https://support.google.com/accounts/answer/185833?hl=en.

You can create an App Password at https://myaccount.google.com/apppasswords