Controlling light switch which uses a relay

I have a push button light switch (pictured on left) which has two wires. This is the type of push button which is equipped with a spring mechanism that enable the button to return to its original position.
When tap it once light are on. A second tap and lights turn off.

I measure about 29V when the button is not pushed down. When I tap it the voltage drops momentarily down to 0V. The lights then turn on if they were off. If the light were already on they turn off.

All wires go to a "utility room" where there is a relay in a relay enclosure just like pictured on the right. It makes a clicking sound when light switch is tapped.

I'd like to have an Arduino control lights. I am not sure what is the best way and how. Should I connect Arduino to the light switch or to the utility room? And how do I manage the 30V issue?
I would also like to record when lights are on and off.