How to trigger an alarm when toilet paper is low?
Bring up several rolls at a time and hang one for use. Put the other two on a short vertical pole within reach of the sitter. Sitter can take another roll when needed. 

Mechanically sense lack of weight on the shelf at the bottom of the pole. Alarm triggers when the last roll is removed. No one has to get caught short.

To sense the weight use a force sensitive resistor such as the FSR 400 (see datasheet). Alternatively, you could use a lightweight coil spring to rest the toilet paper on with a micro switch that is released when both rolls are removed. Another option would be an IR beam break detector where the circuit is completed when the last roll is removed.