At times you wish not to chat with your contact friends, family and colleagues and wish to remain unavailable
to them. If you are presently going through any such situation then you can use the
given steps to sign out of Google Chat:
To Sign out of Gmail:
1. Beneath Chat option there is an option of ‘Set status here’, click on the arrow beside this option.
2. Choose the option ‘Sign out of chat’ from there.
To sign out of Google+
1. Click on the arrow beside your status which is available beneath Chat search box,
2. Choose the option ‘Sign out of chat’ from there
Your friends and other contact would not recognize whether you are online/IM or not, once you are signed out of your Google account. You also would not be allowed contact your friends and check there online status. If in case you are using any desktop client and login there after logging out of Google chat in Gmail or Google+, then also your contacts can check your online status and can chat with you via desktop client.