Possible error on the popup: You are not authorized to view this resource
Have you entered the Client ID and Secret Key before clicking the Login with Google button?
Are the Client ID and Secret Key correct, created for a web application OAuth2 flow as described above and they really, really, REALLY belong to the API application you created on Google Cloud Platform? Before dismissing this question as too basic – these are examples of mistakes made writing this documentation.
Has the user you are currently logged in with adequate Joomla privileges to edit the plugin options?
If you answered yes to all of the above then probably your Joomla session is broken. Log out from Joomla, log back in and try again.
Possible error on the popup: Google error 400
Error 400 on the popup
If you receive an error 400 _from Google_ when the popup first opens the problem is that you have not entered the correct Authorized Redirect URIs as explained under “Get your API credentials”.
Please correct the redirect URL and try again.
Possible error on the popup: 403, 404 or Joomla error page
You might get an error 403 or 404 or a Joomla error page in the popup after you confirm that you want to link your email address to your application.
The problem is that your server is rejecting Google's
redirection URL because it contains the URL parameter
scope=https://mail.google.com/. As you can see,
Google includes a full, unencoded URL which might trigger the
server's protection.
If you are using our Admin Tools software and its .htaccess Maker, NginX Conf Maker or Web.config Maker feature please go to Components, Admin Tools, click on the .htaccess Maker, NginX Conf Maker or Web.config Maker button (depending on what you are using on your site) and set Protect against common file injection attacks to No. Then click on Save and Create .htaccess. Now you can retry linking your mail account to Akeeba Ticket System. After you're done you can set that option back to Yes if you want.
If you are not using Admin Tools or that did not help please contact your host. They might have to make a server configuration change, e.g. disable an Apache ModSecurity2 server protection rule.