The problem with this idea is getting power for the Arduino.
A light switch is fed with 2 wires which go in series with the light being switched.
When the switch is off, then there is 240 V across the switch which you can power something with.
When the light is switched on by a relay or whatever, there is no voltage avalaible to power whatever is doing the switching.
You have to include a battery somewhere, plus a method of charging it .