Hi thanks for the response. The Google sign-in is accessed this way:
Settings/Account/Google/Sync Now
Sign-in fails and shows a notification. Selecting notification takes me to the sign-in page.
Signed in, and got a message "Have to log in on the web" (this is because I have 2-factor authentication enabled.
Acknowledging that takes me to a "browser" page where I have to re-login and then enter my verification code.
This last browser page does not show up in the Task List. Neither does the original Settings task or the previous sign-in page. None of them show on the task list.
Using an authenticator app to get the verification code and then (within 40s) go through this sequence is very difficult. I somehow managed to do it once.
I tried going through some other app that might require the Google log-in (e.g. YouTube), but that does not work either. The YouTube app is available in the task list, but then you end up going through the whole sign-in process again, and the verification code has already changed by the time you get to the point of entering it (or your memory fails, and you forget the code).
Very bad user experience. I am beginning to experience more and more Google's inability to design good user-experiences. It ended with their first - the elegant search page. Google Talk was good too, but it is now gone. Pardon the rant.