Thanks F2, W0lle and Fox. As usual, it turned out to be very simple (or there are two very simple ways, really!).
Where would we be without good forum help!?
I've uploaded a Tutorial Mission to help others see how to do this (attached).
You also see a video version of the tutorial on YouTube here: http://www.youtube.com/watch?v=GSfymMCgwIU.
[edit by Foxhound]
Here it is:
This mission is a brief editing tutorial on how to fire triggers via a specific person or unit. It shows two ways. The first is by using the "Grouping" method to attach a trigger to a unit. The second is by using the unit's name.
If you "play" the mission, it will walk you through how these effects work in game. If you then look at it in the editor, you can see the details of how it works.
In the first method, you attach a trigger to an individual by getting into Group mode in the editor and click-dragging a line to the unit. After you do that, you get some options. If you look at the Activation box after you connect them, you'll see that new options appear. It will no longer give you options like OpFor, BlueFor, Anybody, Radio Alpha, etc. Now it says Vehicle, Whole Group, Group Leader, or Any Member. This is fairly straightforward; it gives you a lot of variation for how the trigger gets thrown.
The second method is simpler but limited. It just checks for the individual unit's name. Note that the Activation box is set to "Anybody" for this approach.
There are lots more options/variations (like detecting when a unit enters a vehicle, when a unit is dead, etc.), but for this tutorial, I'll leave it at this.