C++ different template specialisation for constuctor with vectors of unknown type

I'm trying to make a constructor in a templated class act differently if its template parameter is a vector, but am getting an error on the second definition saying "template argument list must match the parameter list". This is what my code looks like:

template<typename T>
class Test
{
    Test();
};

template<typename T>
Test<T>::Test() { /* non-vector stuff */ };

template<typename T>
Test<std::vector<T>>::Test() { /* vector stuff */ };

Does anyone know how to do this?