I've caught myself doing it and I hate it. My Mum always does it and it's irritating, due to the fact that she'll stop listening to me, to stare at someone. If I stop speaking, she doesn't appear to notice, so I know she's focused on the other person and has lost her focus on me. Then there's the worry that the person will realise they're being stared at and get angry or upset. My Gran (her Mum) was exactly the same. My Dad sees my Mum turning into his MIL, because of this trait.
So, I know how annoying it can be and how bad it must look, to those being stared at. Yet, I think I'm starting to do it too. I was sitting in a cafe on Saturday and two people came in. One was a woman and the other looked like a woman of around 60, but she was wearing men's clothes, including men's brogues (they did a little tap dance, whilst wiping their shoes on the mat, so I couldn't help but notice the shoes). I was just curious as to whether the person was a man or a woman, as this is quite unusual, and I must have turned my head as they passed. I caught myself still looking at the person, once they had sat down. I was quite embarrassed, when I realised what I had done and tried to make it look like I had been looking out of the window. Of course, the person was probably a transvestite or transexual and I'm completely comfortable with that. The couple were probably used to people staring, with some starers making judgements about them. I was only (subconsciously) trying to work out what I was seeing.
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"We act as though comfort and luxury were the chief requirements of life, when all we need to make us really happy is something to be enthusiatic about." Charles Kingsley