I figured it out. I believe the plastic housing is not rigid enough. When I tightened down the mounting bolts, it distorted the casing just enough that the switch would not disengage in the off position. I backed-off the lock nuts a bit until the continuity meter would stop sounding when the switch was in the off position. I then applied some blue locktite and hand-tightened the locknuts. It appears to be working now, but I'll have to keep an eye on it after a few hours of road use.

So, lesson learned: if you're using a Hella brand disconnect, don't overtighten the mounting bolts, and double-check the functionality of the switch.