How do I set my Page's messaging status to away on Facebook?

You can set your Page’s messaging status to away for up to 12 hours. Anyone can see that your Page is away in the About section on the right side of your Page.
To set your Page's messaging status to away:
  1. From your News Feed, click Pages in the left menu.
  2. Go to your Page.
  3. Click Inbox at the top of your Page.
  4. In the left menu, click and then select Away.
Note: Messages received when your Page is away aren't included in your Page's response rate or response time.