How to make automatic logout from google account when you close the browser?

Question

Google

We use gmail as corporate mail on our domain. The problem is that the user remains logged into his google account after closing the browser, the next time the browser starts, logging into gmail occurs without a password. The task is to make it so that when the browser is closed, the google account is logged out. Moreover, the user should not be able to cancel this setting.
Googling on the topic showed that this question, in various variations, has been asked many times on google forums, but the Good Corporation remains silent.
What has been tried:
* Forced clearing of cookies, exposed through group policies Chrome. It works, but when using two-factor authentication, each time you need to enter a code from SMS / Google Authenticator'a. It's a chore.
* Addon "Auto Logout" for Chrome - it seems to clean cookies corny, the result is similar to the previous paragraph, and only in Chrome.
* Searching for apps in the Google Apps Marketplace did not return any results
Any ideas?

Answer 1

Log in from a private window

Answer 2

Don't check the "Remember me" checkbox when logging in. The computer will remain authorized for two-factor, but it will exit when you close it.