A blog from the city of gentle winds wouldn't be complete without a post on the cabeceo. Tango and Chaos has a page devoted to it, and Irene and Man Yung have recently posted a long and amusing guide. What I say may differ in details, but we come from different viewpoints. For instance, the Tango and Chaos guide is written from a portena viewpoint, which might not be so helpful to a visiting male.
I guess my experience of cabeceo is coloured by the fact that the first time I really became aware of it was when a local woman turned and made eye contact with me at a milonga, so I've retained the idea that women ask men to dance. I know it works both ways, but I'm inclined to approach it from that direction. Cabeceo certainly gives women a lot of control. If they don't choose to return your glance, you don't get to dance with them, and that's that.
A couple of times recently, women I didn't know have spoken to me in milongas. The first time I was so surprised that this beautiful apparition stopped on her way to the 'banos' and whispered (in castellano): 'Didn't I see you in the class yesterday?' that all I could say was 'Duhhh?', or something similar. Then a few nights ago two women were sitting in front of me. They got up, one turned to me and said something I couldn't follow. I thought they were leaving and tried to say 'Sorry I didn't get to dance with you', with a smile. She nodded, repeated that they were going out for a cigarette and would I mind watching their table for them. (I got it that time around.) The first tanda after they returned, she turned to me and we danced. I wonder if both women needed assurance that I was friendly. The first woman didn't get any assurance and walked off into history, while the second got the assurance she needed, and so we danced. This suggests that greeting and smiling at a possible partner, if you have some excuse to do it, isn't by any means taboo, so long as there is no pressure on the woman to dance. I've noticed local guys making discrete (and sometimes not so discrete) comments to ladies who walk past them, to show (hopefully) that they are good company for a tanda, but you really can't go wrong by smiling.
I'd never stare at a woman: it's not comfortable for me, and probably not for her. It seems to be about glances, not stares. A woman might well have a dance card filled out for most of the evening: a vals tanda with x, D'Agostino with x or y, milonga with z. They don't know me, so I don't enter into it. But x,y, and z might not come through for them, so they'll glance around, perhaps a bit timidly, to see if there's anyone else who will do instead. That's when I'm keeping my peripheral vision as open as possible, so if I sense someone glancing in my direction, I'm ready to respond. It often seems to work in two stages: there's an initial, passing eye contact, and then a moment, or even a tanda later, or even perhaps the next evening, a more positive invitation/acceptance. The unknown is always a problem: what will my friends say if they see me dancing with a complete idiot? Guys have to accept that women need to be able to trust them.
If your distance vision isn't good, get a discrete pair of glasses. In addition to showing you the detail you need, they also convey the message that you are actively looking for someone to dance with. Contact lenses don't have the same effect.
Problems arise when ladies are seated in a row in front of the guys. I haven't found a solution to that one, apart from walking round to where I can make eye contact. But if the guys are seated in front of the ladies, I've noticed that the ladies have developed a simple strategy, which consists of making little balls of paper and throwing them at the necks of the guys to get them to turn round... It's OK among friends!