the brake switch on those is buried inside the "C" of the frame rail, left side, behind/under the floorboard. It is in an area that is common to get dirt/grass/poo in there, which does 2 things. First, it will sometimes just stick. Secondly (and most commonly) the juices from the cut grass clippings will tear the switch up internally, and it just dies. Replacing it requires removal of the floorboaard, and frankly it's not a bad idea to pull the floor off anyway so you can clean in there. It gets nasty. You'll see what I mean (if you haven't already).
BTW, Dave, the controller doesn't shut the engine off if within 2 seconds of releasing the park brake. It will, however, turn the engine off within 2 seconds IF the control arms are moved from neutral and the brake is not released. Didn't know if you knew that or not, but ya do now!
It has a delay in the system, which does several things.
Lastly, I've run into similar issues with ZD21, 25, and ZD28. Possibly others that I can't remember OTOH, but I DO remember those. It's almost always a bad ground on those, and it's almost always in the harness somewhere. I've found it a couple times, other times the owner said "just replace the harness", which is a better fix anyway. The ones I found; I found an issue at a tap in the ground circuit; where a main ground had another wire tapped into it at a "tee" junction. The tee connection runs to the controller, which then allows the controller to do it's job as designed. Fix ground? Problem solved. Worth mentioning because it can cause all kinds of weird stuff to happen, as grounds (or failing/failed grounds) often do.