My, my my, let's not all get hot under the collar about an exercise which has taken on a name of fin pivot. If the exercise is usefull or not is up for discussion. It is the first step to introduction of breath control and to demonstrate the effect of it. However, to "pivot" is to rotate. Even according to Webster's definition. What it is practiced now, and I don't care what the manuals call it, regardless of the agency, is not a fin pivot but a fin hover. A fin pivot is the next step. To hover at the tips of the fins and then rotating on the fin tips 360 deg, maintaining the hover angle. Thus fin pivot.
It's all trivial now, lost in the wind. Most divers nowadays are over weighted 5-10 lb or more. Breath control? It's rather breath holding. Inhale, hold, rise, exhale, drop, etc.
Neutral boyancy is a skill, a monkey can learn that. Just add air to compensate for the lead. Boyancy control is another story, it's an art and it takes a long time to master. Here's a starting exercise to practice. Fins off, mask off, hover in mid water column with the head couple inches below the surface, breathe normally for couple minutes, put the mask back on and clear it, without changing depth more than couple inches down and the head never breaks the water surface through the whole process.