If you are using Gmail app on your phone and you have added your Gmail account/accounts there and now you want to sign out of your Gmail account on your phone then the only way to sign out of your Gmail app is to remove all your Gmail accounts from your phone. To remove your account, follow below steps:
When you remove an account, it removes your Gmail account from all apps on your phone. When your account is removed, you won’t be signed in to any Google products, like Maps or YouTube on your phone also. So, this option is good if you want to remove personal information from your phone before you give it to someone else.
You should note that removing the account from your phone does not delete the account itself, so you'll still be able to use it on a computer or other devices.
From the desktop you just need to click on “Sign Out” to log out of your Gmail account. On your Mobile website of Google you need to tap the menu at the top left of the screen and then taps your email address and then choose “Sign out of all accounts”.
If you are using Gmail app then as mentioned above you need to remove your account to log out of your Gmail account on your phone.
On the support page of Google you can get technical support for Gmail account. You can also get help via live chat or via email. Else you can dial Gmail technical support helpline number.
Gmail Customer Care Team happily answers all the queries and issues of the users at any time of the day. So dial Gmail Customer Care Number as and when you need.