Hi Janne
As long as your behavior script file is in the scene assets and it is a valid script (that can be executed with no syntax errors), your behavior class name should appear in the list.
The video tutorial is a bit old but still mostly valid. These days you also have the option, when you create a new file, to set the file type to "Behavior". This will automatically add the script to the scene assets for you, and (optionally) you can have your file pre-filled with a simple behavior template. In fact this is the recommended way of doing it, it helps avoid some common mistakes.
One thing to watch out for, is that you should use the syntax
MyBehavior = function() {...);
and not
function MyBehavior() {...}
The latter doesn't create a global variable name, so the editor cannot know that it exists and cannot show it in the list.