The current definition of the C++ language speaks about nondeduced contexts only in terms of deducing template arguments from a type 13.10.3.6 [temp.deduct.type] paragraph 4. Those cases, however, don't seem to be the only ones when template argument deduction is not possible. The example below illustrates that:

namespace  A  {
   enum  ae  {   };
   template<class R, class A>
   int  foo(ae, R(*)(A))
   {   return  1;   }
}

template<typename T>
void  tfoo(T)
{   }

template<typename T>
int  tfoo(T)
{   return  1;   }

/*int  tfoo(int)
{   return  1;   }*/

int  main()
{
   A::ae   a;
   foo(a, &tfoo);
}

Here argument-dependent name lookup finds the function template 'A::foo' as a candidate function. None of the function template's function parameter types constitutes a nondeduced context as per 13.10.3.6 [temp.deduct.type] paragraph 4. And yet, quite clearly, argument deduction is not possible in this context. Furthermore it is not clear what a conforming implementation shall do when the definition of the non-template function '::tfoo' is uncommented.