Suggested resolution:

I think we should say:

explicit-instantiation:
type-specifier-seq_opt declarator_opt ;

[Steve Adamczyk: presumably, this should have template at the beginning.]

and then say that:

• The declarator can be omitted only when the type-specifier-seq consists solely of an elaborated-type-specifier for a class type, in which case the instantiation is for the named class. If the declarator is present the instantiation is for the named entity.
• The type-specifier-seq can be omitted only when the declarator is for a constructor, destructor, or conversion operator.
• The type-specifier-seq cannot define any new types.

There are similar problems in 13.9.4 [temp.expl.spec]:

explicit-specialization:
template <> declaration

Here, I think we want:

explicit-specialization:
decl-specifier-seq_opt init-declarator_opt ;

with similar restrictions as above.

[Steve Adamczyk: This also needs to have template <> at the beginning, possibly repeated.]

13.9.3 [temp.explicit] defines an explicit instantiation as

explicit-instantiation:
template declaration

Syntactically, that allows things like:

    template int S<int>::i = 5, S<int>::j = 7;

which isn't what anyone actually expects. As far as I can tell, nothing in the standard explicitly forbids this, as written. Syntactically, this also allows:

    template namespace N { void f(); }

although perhaps the surrounding context is enough to suggest that this is invalid.