I tried logging out the account on Gmail, but it logged out the Play Store as well. How can I logout of my Gmail account without logging out of the Google Play Store? Is it possible?
It is not possible according to this guide https://support.google.com/mail/answer/2991620?hl=en
There’s no option to sign out of the Gmail app for Android without removing your entire account from your phone or tablet. However, you can accomplish many of the same tasks through other actions, depending on what you need.
As an example you can disable Gmail sync and just check your email from the web browser.