You can roll a dice for the movement of the Zombie King. 8 Sided one, where the count begins with the side that had the King, with a clockwise movement.
If an 8-sided dice is not available you an use a 6-sided one, where 2 of the players can remove 1 freedom of movement for the king.
      
You may have seen my recent post on 4PC Numerical Notation; the main impetus for this being correspondance games between international fellows who may be acustomed to different symbols representing different concepts (henseforth a Universal notation to avoid all confusion).
It brings up the question of how we should canonize Zombie King movement, or what should we do with a players King if in the correspondance (FFA or Solo) game they should resign?
I'm talking very specifically about scenarios when we do not have available an engine to make the moves for us, for example, a correspondance game conducted via letter or email. Is a Zombie King even tenable?
Feel free to discuss your ideas and solutions here. After enough time and/or discussion we'll define a standard for correspondance games (both 1pt queen and QRBN).