I have to do something and need advice.

It's about the girl i talked about in my other post. I wrote it in venting-mode, so i'll resume it here: Roughly a few months ago a very beautiful girl at the Gym started giving me lots of signals. Especially intense eye contact and hovering around me. I wanted to make some move but was paralyzed and couldn't do anything other than engaging in the eye contact that she always initiated. I guess she has kinda given up for a bit with this approach . But lately she has started doing this thing that she pretends to (one time i clearly saw her peeping at me while i was about to walk past her and akwardly timed to start walking) unintentially cross my path and , when i give her way (as i practically always do with anyone), she turns, waves at me and says "Sorry/excuse me" . If i'm not crazy, these are still signals, right?

I have tried to talk to her a few times with the excuse of using a machine, but she seems to be as nervous and intimated as i am, which kinda killed the little momentum i had.

But this thing has bene consuming me, and life sucks more than usual. I need closure.

How do i approach her at this very weird stage? Trying to start with some small talk (like i could...) as tho nothing happened feels wrong. But a direct approach ater the heavy signaling has stopped seems too late.

Thanks for reading. I tried to keep it short. Ask me anything. Any advice will be appreciated.

PS: Is there any point at all anyway when i have zero social skills and capability to connect to people left?