How does ひらひら and 構う function in this context?


In the visual novel Rewrite, there is a conversation between 咲夜, ちはや and 瑚太郎
(the MC)

Context: This is 咲夜’s first scene in the game, and so far the only thing we
know about him is that he is somehow involved with ちはや. 瑚太郎 tries to ask him
what he really is, but doesn’t really get too much information. This is how
the conversation goes:

> 咲夜 -「そうですね…言うなれば私はちはやさんの」  
> 「ナイト」  
>  「といったところでしょうか」  
>  瑚太郎 -「…はあ、そうですか」  
>  詮索する気が失せた…。  
>  暖簾に腕押しってワケではないが、なんかひらひらしたのに構ってても、結局何にも得られないような気がする。

What does “ひらひらしたのに構ってても” mean exactly?

I didn’t find a relevant meaning for ひらひら, and I am also confused why it’s in
past tense, nominalised with の, and used with に構う?




  * This use of ひらひら makes little sense by itself, but it is supposed to be understood in conjunction with the idiom [暖簾に腕押し](https://japanesequizzes.com/portfolio/noren-ni-udeoshi/) in the same sentence. [暖簾](https://en.wikipedia.org/wiki/Noren) is clearly associated with ひらひら.
  * For the grammar of this (と)した, see: [Meaning of (と)した in やんわりとした暖房](https://japanese.stackexchange.com/q/74965/5010)
  * This の is not a nominalizer but a substitute for 人, or "one".

So ひらひらしたの is the same as ひらひら(と)した **人** or literally, "a fluttering one". It
actually refers to "a _noren_ -like person" in this context. This is a unique
description of someone who does not give concrete feedback when you throw
words at him. Another example of ひらひらとした物 is a bullfighter's cape, so you may
imagine it to grasp the feeling of the sentence.




  * This use of ひらひら makes little sense by itself, but it is supposed to be understood in conjunction with the idiom [暖簾に腕押し](https://japanesequizzes.com/portfolio/noren-ni-udeoshi/) in the same sentence. [暖簾](https://en.wikipedia.org/wiki/Noren) is clearly associated with ひらひら.
  * For the grammar of this (と)した, see: [Meaning of (と)した in やんわりとした暖房](https://japanese.stackexchange.com/q/74965/5010)
  * This の is not a nominalizer but a substitute for 人, or "one".

So ひらひらしたの is the same as ひらひら(と)した **人** or literally, "a fluttering one". It
actually refers to "a _noren_ -like person" in this context. This is a unique
description of someone who does not give concrete feedback when you throw
words at him. Another example of ひらひらとした物 is a bullfighter's cape, so you may
imagine it to grasp the feeling of the sentence.

