A little update; I have replaced the dipping mirror with the original one and, happily, the alarm/remote locking works again.
It would seem, then, that although the original mirror doesn't auto dip, it does have a receiver for the alarm system, or at the very least, some kind of (dummy) circuitry that the alarm requires.
My plan, when I find some time, is to open up both mirrors and see if I can marry the circuitry from my original mirror to the auto dipping mirror.
The auto dipping mirror is a nice feature; the mirror darkens, when cars behind you have their headlights on. It works very unobtrusively and makes the mirror easier to view at night.
If you take a look at your current mirror you will probably see that wiring is in place. It seems a plug-and-play job, although I need to resolve the alarm issue.