If the stuff is coming at us from “fast rotating bodies such as neutron stars and black holes” then why aren’t they constant signals?
Do the neutron stars and black holes turn on and off? Do they stop rapidly rotating? Do they hop around and shoot their signals at other places in the galactic map?
They dont turn off and on, but the period of the rotation (or a harmonic of it) is revealed in the period of the burst. Think of a spinning and nutating top, and the burst peak is nutating back towards us every 16 days. Absent atmospheric friction, motion in space can be very predictable and repeatable, and takes millions of years to ‘wind down’.
They occlude each other as they orbit.