Ring Doorbell and Servant's Bell

I have a servant’s bell which is manually ‘shaken’ by a small AC motor - like this (http://www.antique-door-bells.com/transformer-info.html). Previously a standard push button at the front door has completed the circuit and powered the motor.

A couple of years ago I bought my Ring Video Doorbell and it’s been on my list to work out how to hook up the AC motor to respond to a press on the Ring since!

I’ve tried simply swapping the Ring in for the push button (which doesn’t work) and including the diode (which makes the motor turn and ‘shake’ the bell continuously). It’s clearly not a standard or ‘approved’ chime (!) but is anyone up to the challenge and have any advice?!