Did you go to demo.Moodle.net and see if your site gives the same views? Enable mobile web services in MoodleDocs (which I researching) gives the same steps. You do not need to go to advanced settings first. When you go to the External service and check the box and save the page, it will turn it on in Advanced Settings.
In > External services you should see a check box for Moodle and something under it for Built in Services (with moodle plugin) and Custom services (blank but with the add link). I am seeing this in demo.moodle.net . If you are not, then perhaps you do not have the permissions to see it or your moodle code needs to be updated, or reinstalled.
Hope this helps. Now if I can borrow my daughters phone to see how this really works Chris