No, you don't need to know the singleton's type. You can have several implementations of an interface, each of which is a singleton. Then you have a reference to the interface type, which allows different methods to be selected.
Ah yes, the fabled multisingleton, because once you've dug your hole there's nothing better than filling it with raw sewage, and once you've got a singleton you can fill it up with half a dozen interfaces because reasons.
