These pictures were shot through a magnifying glass, which explains the curved edge sometimes seen.
These terms, "tightening" and "finishing," are words I'm using for my own convenience. Like so much of braiding technology (and model tackmaking!), there isn't really a standard terminology. I was influenced by Gail Hought and Tom Hall, not to mention the great pioneer Bruce Grant. I had to have some means of distinguishing the various steps I use to make a miniature braided button, so I borrowed and invented.
Finishing is the art of securing the thread ends in such a way that they don't pull loose and can't be seen. You gotta fix 'em, hold 'em and hide 'em. You sure don't want to bulk up the button in doing so; but the absolute worst thing that could happen is they'd pull out somehow. "Know when to hold em, know when to fold em." Just tying ends together adds terrible bulk, but merely tucking under doesn't quite hold them; and how I hate glue! The skill of finishing could be the heart of the TSII's one-ninth-scale model braidwork.
When we last saw this button, after tightening, it looked like this:
It doesn't really matter which end finishes first. Neatness and convenience weigh in at this stage: whichever presents itself best and most clearly. Look for flattest in relation to the lace (it's much harder to finish around corners or over edges). It's convenient to me to do each color separately; for example, here, blue and blue then black and black.
Beginning with the long end of the interweave (the light color), I aim the needle back into and underneath the button, in the direction that thread came from. The needle goes in first without any thread. I thread the needle after I'm satisfied with where it's going.
Note how the needle emerges inside of (buried within) a light color pass. It could just as easily have gone into the pass above the one it did; two or three passes up from the end of the button is ideal. I would not have used the end pass (too shallow an angle of attack, and not enough thread to hold). Four passes up is too steep an angle for my taste, and risks bulk.
To finish this button it is necessary to re-thread the needle four times, once for each thread end. This dictates the length of the shortest end: long enough to re-thread the needle with. I can't tell you how many times I've gotten short ends too short. Then, you push the needle through as far as you dare, lick the little stub end of the thread, manuever eye and thread like crazy and hope you've got steady hands.
Now for the short end of the same color. In this photo the needle is already threaded.
Tension, of course, matters: too much pull and you'll get wrinkles and bulges. Too little tension and you'll have leather showing and loops sticking up. You should have gotten a sense of even tension while braiding; the same gentle but firm tug will do the job here.
Now for the black, the foundation button ends:
Alas, no pictures exist of the next step: clipping the ends. Some skill is required here, but mostly everything depends on the sharpness of your scissors! Cut the thread ends flush, and throw them away. Try not to cut the button itself. Ideally the button thread fibres close over the exit points and nothing can be seen. At this scale and with these materials, less than perfect often does just fine.
I have chosen the longest button on this breastcollar because it was the easiest to photograph and show everything. It's a 21P 4B with 9 rings. The principles of braiding, tightening and finishing apply to any length button in this scale (Breyer Traditional) made of cotton and cotton-type threads. Naturally this implies there is a limit on how small one can get. Indeed, I have a "smallest button" in my collection of button formulae: it is the 4P 3B.
But more on that later.