You could simplify it to some degree: simply make a copy of the dungeon map and write down the numbers 2 to 12 at random in various tiles of the map, at about 4 tiles apart each time. Roll 2D6 at the start to determine where the patrol begins (and since 2D6 gravitates towards 7, it's best to put 7, as well as 6 and 8 diametrically opposed from the Heroes' entry location - but that's up to the EW). Then, during each of the EW's turns, roll 1 combat die to see where the patrol is heading:
= move to the next numbered tile, in the direction of the Heroes
= move to the next numbered tile, away from the Heroes
= the patrol remains standing where it is
Saves you the hassle of the magnetic board, all you need to do is keep track of which numbered tile the patrol is at; you could simply write down the number. You can have the patrol move through rooms that way, too, so you can even use this mechanic in maps that are low on (connected) corridors. Your patrol route also doesn't have to form a closed loop, as a line that's traversed up and down works just as well.
Furthermore, you might also want to consider what the patrol does when it hears combat sounds from a room or corridor next to the location they're in.