Quoted from EM-PINMAN:It will work fine in all directions just as the original was of the same design. Great work all around by the way.
I have never seen a flat Stylus used for bi-directional gun positioning. They are usually found on stepper units. By logic, it is not designed to move side to side. Only in the direction of the ice skate. Gun stylus are rounded, pointed things so they can change direction at any angle. If the flat one hits the edge of one of the traces on the PCB, it will either start to attack the trace/dot, or the trace will bend the stylus.
The ones you linked to on flippers.com you will notice are the pointed ones. And every gun stylus photo I have ever seen uses rounded ones.
I could be wrong, but I would not use the flat one for any length of time if I were you.
I know its Williams but here is what the normal gun stylus look like:
https://pinside.com/pinball/forum/topic/gun-game-stylus-replacement