How to Prevent Gmail From Revealing Your Online Status

When you communicate through Google Hangouts with one of your contacts, Gmail adds them to the panel on the left of the email screen for fast and convenient access. You just click a name or image in the panel to open a chat window where you can start a text or video chat. You can see when any of these Hangout contacts is online on the panel. They can see when you are online, too.

Your friend or colleague can automatically see when you are online throughout the Google Talk network—via Gmail, for example—and available for chat.

If you can forego that convenience and would rather decide for yourself when your contacts can tell whether you are online, Gmail provides this level of control as well. 

To protect your online status from being revealed automatically in Gmail and turn off the chat feature for all your contacts.

If you only want to mute the notifications of chat for a short time while you are busy, click your profile picture in the left panel of Gmail and use the drop-down menu next to Mute notifications for and select a time period from one hour up to one week.

There used to be an invisible mode in Google Chat, which was the predecessor to Hangouts. Invisible status isn't available in Hangouts. You do have some control over who contacts you. Click your profile picture in the Gmail left panel and select Customized Invite Settings. These settings contain controls that allow specified groups of people to contact you directly or send you an invitation.