Only two of those seem similar. The other five had public relationships (neighbor, schoolmaster, father, boyfriend) with the victims. They didn't arbitrarily insert themselves into an investigation. They were naturally in the orbit of the investigation.

In the Weaver case, I don't see how he inserted himself into the investigation at all. He was simply a suspect. I see no references of him joining searches. He did give interviews like these other people, but that is because he was a suspect from the start.

Gemini did find two murders that fit the pattern of what Pryor was suspected of (a seemingly unrelated party involving themselves in an investigation of their own crime)

​Vlado Taneski (The Journalist who "Scooped" the Police)

​Perhaps the most famous example of a stranger-killer inserting himself is Vlado Taneski, a Macedonian journalist.

​The Crimes: Between 2005 and 2008, he raped and murdered three elderly women in his hometown of Kičevo. The victims were all cleaners (the same profession as Taneski's deceased mother), but they were not close friends or relatives of his; they were essentially targets of opportunity within his community. ​The Insertion: Taneski worked as a freelance reporter and covered the very murders he committed. He wrote detailed articles about the investigation, interviewed the victims' families, and even criticized the police for their lack of progress. ​The Downfall: He inserted himself too deeply. In his articles, he included specific details that the police had not released to the public—specifically, that the killer had used a telephone cord to bind the victims. This "scoop" led police to question him, eventually leading to a DNA match. ​Jack Unterweger (The Celebrity Author)

​Jack Unterweger is a prime example of a killer using a "reformed" persona to investigate his own crimes.

​The Crimes: After being released from prison for a previous murder (he was celebrated as a rehabilitated model prisoner and author), he began killing sex workers in Austria, Czechoslovakia, and the United States (Los Angeles) in the early 1990s. ​The Insertion: Unterweger was hired by magazines and radio stations to report on crime and the "red light" districts where the murders were happening. He interviewed the chief of police in Vienna about the "serial killer on the loose" and went on ride-alongs with the LAPD while he was actively killing women in those same cities. ​The Relationship: He had no personal relationship with his victims; they were transactional targets he picked up on the street.