Perhaps bolstered by my recent reading, I bit the bullet today and deleted the strangely now duplicated gmail account from the Mail program. How there came to be a duplicate of it under the Notes folder, I do not know. I do know that it was indeed constantly re-getting the mail for that “second” version. Or so it seemed to me. So I took a breath and reviewed all appropriate clichés and said “yes computer, please delete that account. Yes I know everything associated will be deleted from my computer but deep in my heart I am confident that everything I really need and, oh!, so much more are still safe and sound on Gmail’s voluminous email servers.” Recreated the account in seconds and voilà the problem is solved.
Now a nice once through of “downloading” the mail. It will go through the rules and filters and end up, pretty much right where it all was before.
Oh that the rest of life were so simple, eh?