A group of transients was staying at a motel near the little girl's home on South Lorimier Street when Elizabeth, known to her family as Beth, disappeared while playing in the yard.
At the time, family members told police they had seen members of the group try to coax Beth to their car -- which was traced to a dealership in Michigan -- twice in the days before she vanished.
The group had ordered a part to be picked up from a Cape Girardeau auto dealership on Monday, but they left town shortly after Beth disappeared.
Mark Harper, co-founder of Indiana-based MJA Inc. Investigations, was looking into another missing-person case when his research led him to a campground near Monroe, Mich., operated by a family of "gypsy travelers" whose wanderings seemed to overlap those of the people who owned the car seen outside the Gill home in 1965.
The campground itself was just a few miles from the dealership to which the car was traced in 1965, Harper said.
Beth's sister Martha Hamilton said several years ago, investigators found a relative of the people who had been driving the car.
The relative confirmed her family had been in Cape Girardeau when Beth disappeared, but everyone involved was deceased, with the exception of an elderly woman who had Alzheimer's disease and thus couldn't provide any information, Hamilton said.
Harper said the people may be dead, but their stories likely aren't.
Members of traveling clans typically pass down their histories to the next generation, so it's likely someone in the family knows what happened and where Beth is, even if the people directly involved don't, he said.
Someone might carry part of the story in her genes.
While investigating the other missing-person case, Harper spoke with two men who said it was not uncommon for their family to abduct children and raise them as part of the clan, steering girls into arranged marriages once they reached adolescence, he said.
During his research, Harper found three women about the right age to be Beth's daughters, he said.
At least one has agreed to a DNA test to determine whether she is related to Beth, Harper said.
One of Beth's sisters, Trish Dokich, said she works at a motel and frequently encounters groups of transients who are suspected of being what she termed "scammers."
If Beth was abducted by such a group, it's possible she is alive and well and involved in criminal activity, Dokich acknowledged.
"We always hoped that they would have sold her to some good family that wanted kids," Dokich said, but even if they didn't, "she's still our sister."
Beth's aunt, Carole Glasson, agreed.
"We'd still love her," she said.
"We've all survived each other thus far," Dokich added, laughing.
Detective Jim Smith said criminal charges in the kidnapping case are unlikely at this point, but if one of the perpetrators' descendants was arrested for an unrelated crime, he might be willing to give up Beth's whereabouts in exchange for leniency.
"Cases are made all over the United States just like that of people giving up information when they're incarcerated," Smith said.
Anyone with information about Beth Gill's disappearance can call the Cape Girardeau Police Department at 335-6621.
324 S. Lorimier St., Cape Girardeau, MO