Wow, GREAT topic. I wish I had some good advice.
Sadly, however, I'm struggling with this both in Guitar and in Kendo and Iaido (japanese sword). All three are something where an onlooker would not really think Breathing was all that important, but actually - it is quite critical.
Specific to guitar, I tend to let my breathing and my body tension vary too much while playing, and for some reasons, subconcsiously, when I get near the end of a piece, whether it is a slow soft ending, or a fast, exploding abrupt one, I have a tendency to just let out this huge sigh of a breath as I'm finishing it up. Very annoying, as it just ruins everything because of what it does to the rest of my body.
On a related note, I've also found that pieces that I'm very famliar with, I tend to breath easier, and pieces I'm working on or struggling with, I breath like I'm running a race. Which makes me wonder if breathing and relaxation in general aren't symptoms rather than causes in some ways.
I guess that's analagous to the "face" concept in music, where someone who has a high level of ability can keep a completely relaxed facial expression throughout their playing. That's not to say that you can't make faces and sound great (I've seen a few professional classical guitarists whose face and head swing about as if they are heavy metal performers! haha, but that seems to be the exception), but I've heard music teachers say that part of practice is to keep your facial muscles relaxed while you play, and some high level classical guitarists go so far with that, they look a statue, except for their hands are moving! One time, I thought this one lady was having a "no blink" contest with someone in the audience !!
For me, I find I am typically doing "scrunchy" things with my face without realizing it at the same times I'm doing strange things with my breathing. Again, that's usually on pieces I'm struggling with or learning.