I believe it's the other way around; the original trigger "attached trigger" is left blank. the second trigger has the first trigger in the "attached trigger" box
if you need an actual reference, I know for a fact there is "attached trigger" trigger in the GDI UFO mission where you have to capture the tech center - There is a trigger that makes you lose if it is destroyed, and attached to that is a trigger that makes you win if you capture it.
Double click on the tech center in FinalSun and you'll see it has an attached trigger. then there is another trigger attached to this trigger, since you can't attach more than 1 trigger to any given object.
The way I learned triggers -- especially trains -- is by looking at a map that I've seen a similar trigger being used.
They are a pain to learn, but golly once you learn them you can do all sorts of cool stuff