Posting anon as this is a bit embarrassing/revealing for both myself and any other mums who may know me in real life on here. 
Currently co-parent with ex-wife (amicably - there was no OW or bad behaviour on my part, she says she just fell out of love), so often do school runs. Over the last few weeks I've started noticing one of the other mums, for want of a better term, staring at me. Basically that: just a fixed stare with a slight smile on her face. Sometimes I give a brief acknowledgment but more often than not its from across the playground or assembly hall and so one or the other of us looks away. She never bothers to come and say "Hi" or anything. Just keep catching her staring.
As far as I'm aware she's single too - her ex seems a good guy and IIRC there might be gossip she got involved with someone else. We never socialised with them bar school events, although my wife may have met up with her after we split.
I'm single and not really looking - just getting my life together after the divorce.
I'm a bit clueless about all this and prone to overthinking stuff, so I guess I'd consult other mums who are more experienced with school gate etiquette. Am I reading too much into this? Or is she eyeing me up? I'm not even sure I'd want to "go there" tbh, but it would be good to at least have a better idea as to what on Earth is going on...