Mystery solved.
I Googled the Beechcraft Starship and came up with a very similar looking plane. However the Beechcraft does not have a rudder and this plane does.
So after adding the word "similar" to my search I came up with
Piaggio P-108 Avanti
It turns out it is some Italian Navy/ Army/ Airforce plane.
I wonder what it was doing in the Hamilton area then?