To make your account default to invisible for chat:
1.) Login to your unseen account
2.) Hover the gear/settings button, (located at the top right)
3.) Click on Account Settings
4.) Check mark “Login as Invisible”, (under account privacy)
5.) Click “Update Settings” to save changes made
Your chat default settings will be set to invisible. You will just need to log out and back in to see the changes made.