This article explains how to prevent Gmail from revealing your online status by turning off the chat visibility setting. It includes information on how to mute notifications in Gmail for a period of time.
How to Hide Active Status in Google Chat
Your friend or colleague can see when you are online via the Google network, for example via Gmail, and are available for chat. If you want to control when your contacts can see if you are online, Gmail offers this option.
Here's how to prevent your online status from showing in Gmail and how to turn off chat for all your contacts.
Click the gear icon (Settings) in the top-right corner of any screen in Gmail.