If the declarator declares an explicit instantiation or a partial or explicit specialization, the declarator does not bind a name. If it declares a class member, the terminal name of the declarator-id is not looked up; otherwise, only those lookup results that are nominable in S are considered when identifying any function template specialization being declared ([temp.deduct.decl]).

Consider this example:

void fun(int*, void*);  // #1

template<class T, class U>
void fun(T*, U*);   // #2

template<>
void fun(int*, void*);  // #3

We do not restrict more requirements on the name lookup for fun. The result should consist of #1 and #2. [temp.deduct.decl] p1 says

In a declaration whose declarator-id refers to a specialization of a function template, template argument deduction is performed to identify the specialization to which the declaration refers.

It is not clear whether the declarator-id that is an identifier refers to a specialization of a function template or not. We just say

A template specialization can be referred to by a template-id

in [temp.names] p1. The identifier refers to a specialization only if the deduction succeeds, I think. [temp.deduct.decl] p1 also says

In all these cases, P is the type of the function template being considered as a potential match...

This implies that only function templates are considered when identifying any function template specialization.

[dcl.meaning.general] p3.3 might be changed to

otherwise, only those lookup results that are function templates and are nominable in S are considered when identifying any function template specialization being declared ([temp.deduct.decl]).

change [temp.deduct.decl] p1 to

In explicit instantiations, explicit specializations, and certain friend declarations, template argument deduction is performed to identify the template of which the specialization is being declared/instantiated by the declaration.