Creating a singleton is not just writing a method. The idea is to only ever have one instance of the class: mixing an instance stored in a class property with the ability to create as many instances you like (via __construct) defeats the point of trying to implement the singleton pattern.

I just used empty due to personal preference: "If not empty..." reads better, for me, than "if ... is not equal to null" and there isn't any requirement to be checking only for NULL (is there?). !== null, as you know, would work equally well in this case.