Simple rule: IL must always reciprocate in a relationship or dating.

If she likes you, you showing interest won't be a problem... it's showing too much continual interest.

There is nothing wrong in approaching a girl and subtly letting your intentions known. Unless she is crazy (and therefore not worth dating), indicating YOU are interested in her will not be a turn off if she is already attracted to you. More than likely she'll appreciate you "pulling the trigger' and initiating. That is what us men are expected to do. However, don't overdo it or become an open book. NEVER tell her everything on your mind, simply show mild interest.

Where we go wrong is unconditionally showing increasing interest continually afterward. She should be reading your interest like a line graph; with highs, lows, peaks, etc.

She flakes? Don't be quick to call her again. She gives you a hard time over something? Leave abruptly. I believe in "nexting" women without actually nexting them, it works wonders. And it's not even important that you go tit for that, what's important is that you're not predictably and unconditionally "in it for the long run"...

That's what marriage is for.

What you said can resume my entire relationship game. Simple as that.
Never show more interest than the girl is showing.