Greetings Eric, and welcome to the forum.
I don't think there's a "formal" name for that technique, but Grant (forum co-founder and expert linguist) might jump in and provide one.
Ellipses can be used in a variety of ways, depending on the style of writing. The MLA handbook (and others) is quite specific about how to use them. But it literature it's a whole 'nuther matter, and mainly one of style.
In your example, the ellipsis is clearly used to indicate a pause in thought, and is followed by something worth emphasizing. The fact that they were soldiers says one thing, but after the "pause in thought" Galloway apparently wanted to make the point that not all soldiers are young, but in this case they were young.
It's an effective way to indicate that the writer, after some thought, decided to add more relevant information. For example: We were certain we had the correct route … until the road came to a dead end.
Oh yeah … wistfulness is much better than "a pause in thought." Because during that "pause" the brain ain't stopped. It's just wistfulizing.
So do we answer Eric's original question as wistfulization? I like the sound of that.
On the other hand, the ellipsis can be powerful and melodramatic. The sentence Eric cited fits that category, I'd say.
So in that case, do we answer the question as melodramatization? I don't like the sound of that.
This is getting more interesting the more I think about it. In cases where the ellipsis is not being used to indicate preceding, missing, or following text (where it's referred to as an omission), we don't really have a single term that describes the other use. Do we really need one? Probably not. But it's an interesting Gödel-like exercise to try describing the language with the language. That "pause" can be used for a lot of intentions. I have no idea what single word would describe that type of use. Maybe call it a brain track switch? :) I doubt there's a one-word answer to Eric's question.