Sensor to track book open or not
Don't bother with a proximity sensor. Those are intended to see how far an object is, without touching. In a phone, it's used to measure if your face is close enough to the screen that the screen should turn off.

Needing to know if a book is open or not is so much simpler. Like the way the iPad can tell if the case is closed or not. It uses a magnet and a hall effect sensor. A magnet with a small reed switch can also work.

A simple flex sensor in the spine could work. A light dependent resistor or photoresistor can work as well. Or the simplest method, two pieces of metal that only touch if the cover is closed (A normally closed momentary switch).