I found it out by plugging in an external monitor and Night Shift not working with it. I could believe it is specific to the monitor you have, but judging by Apple support I'm not alone:
The answer implies that it only works on about four different monitors. I doubt that's true but it seems like a shot in the dark to know which it does and does not work with.
Interesting, never heard of that before! I use a 5 year old Dell P2715Q screen and I just enabled / disabled it and it's working fine so that list of screens seems to be outdated.
I have a (probably) related issue on my dual display system where it works on one but not the other, making it just as useless in practice. I still use f.lux as a result.