I think the underlying mechanics is the instrumental music keeps a portion of my brain occupied/ interested in the same way that fidget toys are supposed to while simultaneously blocking environmental distractions.
That has made me remember another trick...I have "wiggle pedals" for my feet. They are similar to an under desk bike pedal device but allow for multidirectional movement. Found them, they're called Hovr. A really good substitute would be those elastic exercise bands stretched over the legs of the chair. Like these...
I have on occasion used the headphones and the Hovr pedals at the same time, and I experienced what can only be described as the Vince McMahon reaction meme (the glowing eyes one). Shame I used that power on drafting board financial reports and not solving global warming, but I didn't have that on my to do list.
This is how I experience it too, and I'm in my 40s. If I don't take it during the week, I burn out so easily.