I would like to add a Sign In with Google and a Sign Out button to my Chrome extension.

One technique that uses chrome.identity.getAuthToken for Sign In is described in this tutorial. It works great! When the button is clicked, it shows a popup for authentication and authorization.
But how should I implement the Sign Out button?
I tried to use the removeCachedAuthToken method in the on-click handler of my Sign Out button. With this, the sign-in functionality doesn't work as expected. After, when I pressed the Sign In button again, I got a new token directly without a popup asking the user to authenticate and authorize my extension. I would like users to be able to change their account by signing out. With this technique, that's not possible. How should I implement the sign out functionality to allow for this?