Wow. I was actually thinking about this today, and was considering posting a thread on here out of curiosity. In New England at least, there seems to be no consensus even among karate schools, let alone Japanese versus Korean versus Filipino versus Chinese. Many schools do the eyes up thing, some even speculating that eye contact demonstrates respect. And it does, in a more general context. In the USA.
My personal take, as a sweeping generalization of the interpretation of area schools, is that bowing is a symbol of respect, which you should strive to hold for everyone and treat everyone with, including your opponents and enemies, but that looking down is a symbol of trust, which can be separate from respect, and should be reserved for those that you are relatively sure are not about to wing you one. Personally, I figure anyone I'm bowing to is someone I've already decided is not imminently about to try to injure me.
Also, from what I recall of Elementary School mandatory Japanese class (aside from Kobayashi Sensei being an excellent teacher) was that the eyes should always look at your toes when bowing.
In many ways I think that, again in New England, many people seem to feel and convey more respect with a handshake or glove tap before sparring, than with a bow. It's just not part of our culture outside of our martial arts schools, and I think in many cases is more something associated specifically with whatever martial art, rather than with mutual respect, whereas the handshake is something which everyone grows up utilizing as a symbol of good will, good faith, respect, and a demonstration of character.
Bowing, in western culture, generally has fewer connotations related to mutual respect and humility, and more which are tied to power disparities, however historically or culturally inaccurate that may be. I know newer students and outside viewers often seem to assume the bowing is intended to demonstrate subordinance to and reverence for the instructor. Regardless of how incorrect this view may be, it's a hard lump to jam down many a Mainer's throat...
For my own part, I find more mutual respect from a grin and a fist bump. Again, none of this has any significance outside of the culture it's being practiced in. The martial art and accompanying social formalities may stem from Japan/Korea/China/Wherever else, but if it's being practiced in a school in Toronto, the culture of that school is probably the most relevant. That said, I remember a Japanese Karate team from Amori coming to visit years ago, and very politely correcting many of the local schools on various matters of butchered culture and pronunciation....
This may be somewhat the viewpoint of someone shaped by practicing a US take on a poorly understood Korean derivative of a somewhat better understood Japanese derivative of an Okinawan art with roots in China. Everything has been so twisted, mixed, bungled and bastardized at this point, that I suppose I lack a certain reverence for tradition. I'm not complaining about the warts, mind you. I just try to remain aware of them.
Point being, there's certainly a great deal to be said for studying the root culture of an art, learning the meanings and significance of traditions, etc, but when, say, I visit a Shaolin Kempo Karate school and they start telling me about the long history of their Pinan Forms, and discuss the long standing pre-class belt tying rules of who kneels and stands and when, I just go with it. When I go to a TKD school and they tell me how and when to bow and to who and why, and the pre-class formalities are in a bizarre mixture of Japanese and Korean, again, I just go with it. the words and formalities and mythologies may be inaccurate and with significance far from the original, but they have a meaning and significance in the culture of that specific school.
Just like I wouldn't bow to someone knocking on my door, just like I wouldn't shake the hand of a young Orthodox Jewish woman on meeting her, just like I wouldn't walk into someone's school, walk to the front of the class and shake hands with the instructor in the middle of class. When you're with a group of people, it's polite to do whatever it is that group of people think is polite, even if it seems silly. Even if that's bowing with eye contact and grunting "Osu" in affirmation every few sentences.
Pointless 3AM ramble concluded.