I've just tested an authorization and re-authorization of a Gmail account and everything went as expected -- so I don't think the problem is necessarily with Google.
I'm running out of ideas here...
You can try this -- but I'm not sure if it is going to make any difference.
Do a right-click on this account in the accounts pane and select "Duplicate account..." from the context menu.
Then when you are in the edit window try an OAuth2 to see if this makes a difference....
If no help once again -- I'll contact Jeff concerning this issue.
Good judgment comes from experience and a lot of that comes from bad judgment. - Will Rogers
If rebooting doesn't work, another experiment to try is to (temporarily) change the email address just before you press the OAuth2 button -- for testing purposes, just delete the email address.
Does that allow you to see the Oauth2 window? Don't bother entering your information; because of the way that PP associates the data, this is not a permanent solution.
lakrsrool's experiment of duplicating the account is a good test, as well.
And I take it the "Duplicate account..." experiment did not help either?
If by duplicating the account by adding say one digit to the "Account name" in the duplicate account and then saving the duplicate account as is (with just the minor "Account name" change) and then have done a "Mail Check" for that duplicate account (i.e. right-click on the duplicate account and selected "Check mail") which would have populated the inbox of the "duplicate account" with the same messages as that of the problematic account's inbox (you are duplicating from) and if at that point you were able to successfully do an OAuth2" on that duplicate account you would then have a working account. At that point you could have then deleted the original account and then changed the "Account name" in the duplicate account to what you had in the deleted account (which is only possible because the original account with the same "Account name" has been deleted) and then continue to use the new "duplicate account" as the "original" account from then on.
Based on what you have posted in this topic you were troubled by the fact that you were getting messages more often than your expectation of 15 minute intervals. As it turns out you were unaware that your accounts were using "IMAP" with "IDLE/push" enabled which is why you were getting messages "pushed" to the inbox instead of every 15 minutes. Perhaps this did not involve all your Gmail accounts....
I have a question -- was this specific account not one of those accounts getting messages randomly (not every 15 minutes)?
What I'm wondering is whether this specific problematic account has in the past always been using "Webmail" (Server type = "Gmail") and so has never used "IMAP"?
What I'm getting at is this specific problematic account may have never used IMAP before (until now when you changed all your accounts to "IMAP") and was an account that had been previously getting messages every 15 minutes therefore had always previously used "Webmail" -- is this your recollection baconcheddar?
If this is all true -- then perhaps there is something odd about this specific account that is in some way impacting "IMAP" and/or the utilization of "OAuth2" (something we would only know about after using "IMAP" for the first time on this account).
For this reason I was hopeful that perhaps the "Duplicate account..." suggestion might have been of some benefit.
Good judgment comes from experience and a lot of that comes from bad judgment. - Will Rogers