Sun Shafts from a single Light Source?

I’ve got a huge problem. I need to cast Sun Shafts for the Sun in one, big open-world scene, but using the Unity’s built-in Sun Shaft creates the shafts from all brightely lit spots (like clouds and lanterns).

How can I set the Sun Shafts to cast from only a single Light Source (the Sun itself, a directional light)?

In the Sun Shafts script check: Rely on Z Buffer? [✓]