And to add to JB's words, the "tailoff" as I (and rocket engineers) call it is just what 2525 said: the last bits of propellant kernels burning out. There are always some that are slower than the others. A small percent of the powder can ignite late. The higher the loading density, the tighter packed the charge and the greater the distance from the primer, the larger that percentage can be. And some powder, as observed above, never lights at all.
But I think that the real experts in the field are almost unanimous that effective burning is signaled by the pressure peak. And I probably could have left out that "almost."
