Moira Anderson, 11, went missing from her home in Coatbridge, North Lanarkshire, in February 1957 while running an errand for her grandmother.
It is widely believed she was abducted and murdered, but her body has never been found. The case remains unsolved, but Sandra Brown believes her late father, convicted paedophile Alexander Gartshore, murdered Moira and dumped her body in a grave at Old Monkland Cemetery.
At the graveyard, forensic experts have started exhuming the family plot of Sinclair Upton, said to be an acquaintance of Gartshore, in a bid to find Moira's remains.
Bus driver Gartshore died in 2006. Mrs Brown told BBC Scotland: "My father was every bit as much of a paedophile as Jimmy Savile ever was.
"My sad conclusion is that Moira is not the only child in the central belt of Scotland who suffered this fate. Whether we find her or not, we know we've looked. I hope to see results in the next few days."
Mrs Brown, who blamed Gartshore for the murder in her book Where There Is Evil, said it was her belief a "paedophile ring" was operating in the area at the time Moira went missing: "Given recent events with Mr Savile, people are realising this is not a modern phenomenon. It has gone on for a long time."
The excavation is being led by Professor Sue Black and a team from the forensic anthropology department at Dundee University.
Police believe the burial plot has three layers, with up to eight people interred there and experts are exploring the possibility that Moira's body may have been dumped under a coffin in the grave, which was thought to have been open around the time of her disappearance.
A sheriff gave police the go-ahead for the exhumation last month, following a petition at Airdrie Sheriff Court from the Moira Anderson Foundation, started in 2000 by Mrs Brown to support children and adults affected by sexual abuse.
Last year Scotland's Lord Advocate Frank Mulholland ordered cold case detectives to reopen the case as a murder.
A large section of the cemetery has been cordoned off, with a large black tent and a series of smaller blue tents erected on the excavation site.