Thank you for the response! Here are the answers to your questions:
>> Edit the user within CB > User Management and confirm their Google ID field has a value as it's responsible for checking what CB account their Google account is linked to to allow login.
Yes, their Google ID field has value.
>> Does it also do this when you register a new user using the Google button?
For this specific implementation of this feature, we actually don't want to allow new user registration with the Google button. We only want existing users to login using their Joomla login, then link their Google account, and then be able to use the "Google Sign In" feature.
If you would like Joomla/FTP access to the site to look around at the code to fix it, let me know and I can send that in a PM.
Thanks again.