Business Hours Settings
The "Business hours" setting allows you to set the days and times in which you have support representatives available. Business Hours are being used in Rules and also they will determine weather your Chat widget will show in Online or Offline mode on your Shopify storefront.
You can access this setting by clicking on "Settings", then in the left side navigation bar click on "Business hours". You can select different time periods for each day or you can use one of the groups for "Weekdays", "Weekend", or "Everyday".
Once you have set your business hours you can now use that criteria in your rules. For example, you could have one auto responder for during business hours and one for outside of business hours. Take a look at the images below for examples of each.
During Business Hours Auto Responder
After Business Hours Auto Responder
Chat online/offline status
The chat status will always depend on your set Business Hours (under your Gorgias dashboard > Settings > Business Hours). Outside of business hours, chat will show in Offline mode. During your business hours, chat will show in Online mode.
Additional information you can find in the following article: Using Gorgias Chat