It’s on the GCD, so if you try to switch it off during the GCD the click won’t register.
For anyone interested about burning rush make macro like this and you can cancel it with a cancelaura macro even when youre in gcd by just pressing it again.
/cancelaura Burning Rush
/cast Burning Rush
If you would like some modifiers and more into the macro can do something like this what I use for mine, just modify it to own needs.
#showtooltip
/cast [nomod] Demonic Circle
/cancelaura [mod:shift] Burning Rush
/cast [mod:shift] Burning Rush
/cast [mod:alt] Soulburn
/cast [mod:alt,@cursor] Demonic Gateway