From my read on this, I'd say that rhyming has a time and place where it's relevant and important, but your lyric isn't such a time and place. Sometimes I see poetry/lyrics where trying to make things rhyme would become artificial and interfere with the communication.
I'm a compulsive "rhymer." It's rare that I write anything that doesn't rhyme. But I can certainly appreciate poetry/lyrics that doesn't rhyme. I wouldn't make any concessions to rhyming in THIS lyric/poem.
That's not a statement that would cover everything you write. It's a "case by case" basis. But this one is perfect like it is to my eyes/ears.
One other thing. I read your lyric before I read your comment/explanation on/of it. I loved it. I don't love it any less after reading your explanation, BUT, now it just means what YOU meant when you wrote it. Before I read your explanation, it meant "something I couldn't quite put my finger on" and "something I had to figure out."
Now, there is nothing left for me to figure out. . . and one of the reasons for re-visiting your lyric is gone. (Same applies to giving "another listen" to a song.
Something I've learned is that what a lyric I've written means to a reader/listener is every bit as important and valid to that listener as what I meant when I wrote it. And many of them WILL see it differently than I meant it. Seldom does it mean to "them" what it meant to me as I wrote it.
As writers, (if we want to be taken seriously as communicators) it's very important to treasure the interpretations of our audience and the thoughts and emotions that we evoke. I'm not saying "don't explain songs." That's always a hard decision for me, and I think for every writer.
But I am saying to be very conscious of treasuring their interpretations, ideas, and emotions.
Hope that helps you as a writer.