This sounds like a very fun essay. Also you can be very creative. I suggest that you let your mind run wild on this one. Let me give you some ideas.
First, it would be pretty scary, if the person on the other line knew what you were doing, as if they were watching you. This would send chills to anyone if they thought about it. It would also make people paranoid. Who is watching? How?
Second, if the phone calls come when the phone is not connected, it would suggest something supernatural. This, too, could add a twist.
Finally, there should be a few deaths. What is a horror movie without a few of them. Good luck.