I've fired rifles with similar "set triggers" or "hair triggers". Usually, you push the first (or second) button in and pull the main trigger until it clicks. Then, just the lightest stroke on the other button will fire the weapon. It really is pretty cool as it reduces the pull to nothing.
It's a pretty rifle. Short, Colonial rifles tended to be pretty long. Funny thing I've noticed about Europe, the horizon (and other obstructions) tend to be closer. Seems like there is always more distance from one field to another, one tree line to another, ect, in the States. But I've seen shorter rifles from the age over here as well. Just not real common. Tend to be lower caliber as well. Down around .30 or so.
Still, a beautiful bit of work. Love the color. Is it an oak variety?