Do you want the girl to pretend that she didn't see you so that you don't feel embarrassed for staring/checking her out? Or is the purpose of you staring at her is for her to look back at you?
I normally just pretend I didn't see even if the guy is cute because I don't want to embarrass him by him knowing I saw him staring at me.
Most Helpful Guy
Most guys with prolonged eye contact are doing so to get a reading on your level of interest. If you seem interested (e. g. eye contact, smile, other inviting body language) then they will approach you.
Your ignoring them/pretending you didn't see, is them just making the conclusion that you aren't interested in talking to them. They therefore won't pursue you, unless they're persistent, and any chance of a relationship is very low.1