AUTHORISATION Error 400: invalid_request (gmail address on mac mail has been rejected by google)

AUTHORISATION Error 400: invalid_request (gmail address on mac mail 10.13.6 has been rejected by google). A well used gmail address has been rejected by google in mac mail. However, a more recent gmail address is ok on mac mail, webmail and on older mobile devices! How can I make Mac Mail more acceptable to google for all gmail addresses? I am awaiting a response from google but feel that this forum might be more appropriate. Maybe some of you have successfully resolved this issue without buying a new computer!