Pi Zero to activate touch sensor

I’ve got a Lidl daylight lamp for my SAD and the on-off button appears to be a capacitive touch sensor - it responds to faint touches and also if I touch the button with a conductor. I’ve been trying to find a way to make it able to switch on at a particular time to act as a sort of alarm/morning brain chemistry activator. It defaults to being off when connected to power so I can’t use a mains timer or anything like that. This leads me to a way to activate the touch sensor without touching it…

I’ve done lots of reading around of people trying to achieve similar results using standard electronics stuff (arduinos, caps, etc) but I can’t find any explanation of how these capacitive touch sensors work that will stick in my head.

So I was hoping somebody may be able to think of a way that I can use a Pi Zero to trigger the touch sensor at a particular time of day. Anyone?