[dcl.init.general] default-initialization vs extern declaration

struct A{
  A(){}
};
extern A a; // #1

For the declaration at #1, should we say since there is no initializer specified for the object, hence default-initialization is applied?

Specifically, Is there any normative rule in the standard that specifies which declaration the initialization will be applied to?
Except for a note [dcl.init.general.note-10], it seems it's unclear whether the initialization is performed(on a declaration).

Could we change [dcl.init.general] p20 to

A simple-declaration that is definition specifies the initialization of a variable, whether from an explicit initializer or by default-initialization, is called the initializing declaration of that variable.

The modification does not impact member-declarations or parameter declarations, and it can clarify the above example.

Start with [dcl.init.general] p20 and note-10, then trace the wording for simple-declarations, definitions, and initializing declarations in the C++ draft. Determine whether the standard clearly assigns default-initialization in the extern example and whether the proposed clarification is normatively appropriate; done means the issue has an agreed resolution and wording.