I went home at lunch and tried a few things.
1) If plugged in and not touching the bicycle, the kill switch doesn't kill the engine at all ... of course, this is to be expected.
2) If plugged in and loosely attached to the handlebars, the kill switch doesn't kill the engine.
3) If I tighten the screw (see picture named KillSwitch-Sketch.jpg) so that the screw touches the handlebars, it kills the engine regardless of whether it is set to "on" or "off".
I also took some photos of the switch itself. I did not use the small rubber tube in the picture at all. I thought it might be the insulator between the switch and the handlebars, but the switch and straps barely make it around the handlebar as it is. I couldn't get it to fit with the rubber tube in there.
I put a call into Staton Inc but they were gone for lunch (I'm guessing since I got the answering machine and it was during the lunch hour). No return call yet.
If you have any ideas, I'm willing to try them. And I'll keep you all posted on what happens.
Thanks!
Tracy