Unintentional eye contact

I'm a dreamer, and sometimes I'll zone out while staring at a fixed point in space; it might be a spot on the ceiling or someone's face, just as long as it's in my line of vision.  Unfortunately this can lead to An Awkward Situation: accidental/unintentional eye contact with a near-stranger.  Usually it's someone I don't know very well.  This is easy to do during orchestra rehearsals, when I daydream and just happen to be staring at whoever is across from me within another instrument section.  I don't study that person's face but merely rest my eye on that person's visage, and inevitably they'll accidentally look my way since I'm probably in their line of vision and...there's that brief moment when we'll look at each other, and then we blink and look away.