This is a finished concept that I doubt many will need but maybe it will inspire some problem solving for you?

I needed to push a button on the back of a network rack once every day. It is not super easy to get behind the rack...so the button pusher was born.

It uses a 36" flex cable pickup tool as the driving cable.

https://www.amazon.com/gp/product/B006ZEOXJY/ref=oh_aui_search_detailpage?ie=UTF8&psc=1

Parts were mounted using 3M VHB tape.

A nyloc nut, 2 washers and a bolt form the pivot. The flex cable is hot melt glued to the holding bracket.

Not very complicated but the concept was sound the geometry of the pusher was key.

I use it every day and it works well.