Earlier quoted context omitted.
If they don't sync to a common clock source, they won't stay in sync for long. Probably not even for a few minutes or so. You'd get the same phenomenon that you see when operating turn signals in traffic. They seem to weave "in and out" of sync. The frequency at which that happens is the beat frequency, i.e. the difference between the two blinking frequencies.
Wouldn't the mains frequency be a common clock source, if nothing else? But presumably these lights at least have battery backup, given the obvious risks in case all of them were to fail at the same time due to a grid issue.
(Doesn't solve the problem if you want them to be in sync phase-wise, i.e. blink at the same time or similar, but at least they won't drift apart, which was what this is about.)