How do I "stop caring" (so that she chases me)?

Anonymous
I understand that girls don't like when we act needy, etc. So right now, I'm trying to "stop caring" in order to make her chase me. I've seen some... results, I guess? She asked me out 3 days ago and yesterday (over text), she randomly texted me about something fun that she did. I'm not saying that she never initiated any text conversations in the past, but it was generally me who did (most of the time). But in the last 4 days, she's been texting me first twice already (which is already more than what she used to).

The problem is, when I reply to her (a few hours later), she always takes a day (or 2) to reply to my message. I don't want to double-text her because, hey, my goal is to make her chase me (not the other way around). How can I make her reply faster to my messages? Is she conscious of what she's doing (is she playing games with me)? But anyway, we're texting on a website that doesn't send push notifications, so maybe that's why it's taking her long to reply to me...

So I know that I should "stop caring"... but what exactly does that mean? Should I let her initiate everything all the time? Should I just reply to her messages?
How do I "stop caring" (so that she chases me)?
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