I teach my students by telling them they should
breath in normally, so in that respect I agree with RJP. Then I define a "normal" inhalation as ~2/3rd full lungs.
The exhalation is a different animal; I tell my students it should be ~twice as long as the inhalation (2 sec in - 4 sec out, 3 sec in - 6 sec out, etc.). The best breathing petite women divers I have timed do ~5 sec in ~10 sec out (4 breaths per minute :shocked2

, which I think causes brain damage, but most are blonde anyway.
If you are breathing in normally, when you exert more you breath in more, and if you double the time of inhalation you then exhale more (longer). I call it a kind of mantra and tell them that
for me breathing this "mantra" helps relax me,
like meditation. If my students have to be brainwashed it might as well be beneficial brainwashing.
The air in the BC is the rough buoyancy adjustment; the lungs are the fine adjustment (as stated already). The optimal adjustment is to change the position of your "range" of inhalation/exhalation. If you ascend ~5' from a "perfect" BC air amount, breathing from the "bottom" of the lungs gives you a more negative net buoyancy (completely empty to ~2/3rd full). If you descend ~5' from a "perfect" BC air amount, breathing from the "top" of the lungs gives you a more positive net buoyancy (completely full to 1/3rd full). In this hypothetical example, a perfect breathing cycle at the in between depth would be from 1/6th empty to 5/6th full and one could theoretically not adjust BC air content for up to 10' depth change.
Perfection is not in the realm of typical human beings, but understanding the "hypothetical perfect" can help with what actually happens in the real world.
Timing the inhalations/exhalations so that you get the required ~2/3rd in/out cycle with the least oscillation of depth is the key (as stated already). Since the time of inhale is different than the time of exhale, it is pretty hard to maintain a constant depth without sometimes exhaling / inhaling early, or exhaling / inhaling late. Now combine this with currents or surge around walls or big reefs and sometimes you have to aggressively exhale to keep from being lifted too much for your BC air content, or inhale aggressively to keep from sinking too much for your BC air content.
The above situations (current or surge at "walls") is where Horizontal trim "only" seems questionable. Not only do I exhale aggressively when being lifted by water, but I "swim down" as needed. "Swimming up" when water is moving down is also helpful, in combination with aggressive inhalation.
I am not claiming this is the only way to describe / teach breathing / buoyancy, but I have had a lot of success describing / teaching it this way.
