macOS Sierra Internet Accounts Google login stuck
Combining part of your solution and part of the solution from Can&#39;t login with Google using Internet Accounts, I got mine to work again by:


Opening Keychain Access > login and searching for 'google', then deleting all the 'accountsync' and 'oauth' entries. The resulted in my Google account being removed from System Preferences > Internet Accounts.
Completing this: https://www.google.com/accounts/UnlockCaptcha


I was then able to go to System Preferences > Internet Accounts and add my Google account back. It showed the spinny wheel on the gray screen for a second, then disappeared and I was in! Mail and Calendar show my Google data now.

I have 2-factor auth enabled.

Another solution to this would be to login to your GMail account via another program that access's macOS's shared accounts, like Calendar.app.