After looking at this question: Can I remotely control the points on PF train tracks? I got the idea of controlling the train track switch handle using a servo motor that will be able to move the yellow handle to both positions.
The included video in that answer: http://www.youtube.com/watch?v=WoNiq5FCd9U Shows the general idea of how to convert the circular motion of the servo motor into a kind of linear movement that will be suitable for the handle.
So it seems that with a set of Lego Technic bricks and an engine - it should be easy to achieve.
My problem is that I want to use an Arduino controller for this, with a cheap and simple servo called SG90: https://www.google.com/search?q=sg90+specifications
So, what I need now, and a way to connect the SG90 motor to a similar kind of construction, to achieve a similar outcome as in the video (and in the question).
Many thanks for that!