I am trying to be disciplined and put documentation on the X-Plane wiki, and limit the blog to announcements, rants, and explanations of what's going on inside X-Plane.
You can read about custom lights here. The short of it is that a custom light is a billboard on an object where you (the author) texture the billboard (with part of the object texture), pick the texture coordinates and color, and optionally run all of these parameters through a dataref* that can modify them.
For named lights, the light texture comes from a texture atlas that Sergio made a few years ago - it's a nice grid 8x8 pretty lights.
So...why can't you use it with custom lights? Why do custom lights use the object texture?
The answer is: future compatibility. Sergio and I are actually already working on a new texture atlas for the sim's built-in lights. (This has been a back-burner project for a while ... I have no idea when we'll actually productize this currently experimental work.) What happens when we create a new texture atlas with all of the lights moved around and scrambled? If your object referenced that texture, the texture coordinates would be incorrect.
Thus, for the lights where you specify texture coordinates (custom lights) you use your own texture. For named lights (where the texture coordinate is generated by X-Plane) it's safe to use ours.
A Dangerous Bug
I found a bug in 940 that's been in the sim for a while now: given the right strange combination of named and custom lights in a row, the sim would accidentally use Sergio's texture atlas rather than the object's texture for custom lights.
This is a mistake, a bug, and it will be fixed in the next 941 release candidate. I certainly hope there aren't any objects out there relying on this erroneous behavior, which violates the OBJ spec and is pretty dangerous from a future compatibility standpoint.
* Dataresfs are normally thought of as data we read, so the idea of using them to "process" data is a bit of a bastardization of the original abstraction. You can read about the dataref scheme in detail here.