"Serial killers" kill serially.
By your definition the Unabomber wasn't a serial killer for the first 15 or so years because his "Manifesto" wasn't published.
Do you think MOST serial killers have an agenda besides killing?
Kindly define "serial killer" in such a manner that leaves out the perpetrator of these sequential, random murders. It should be easy - you seem so sure of yourself.
Thanks.
Arf
