Marshals took old jail mugshots of Jones, now 59, and looked for a match in all driving licences issued by Florida in the decades since his escape. And... snap... there he was on a permit issued to a "Mr Keith" in 1981.
It was a short distance from there to last Thursday. Once he knew the jig was up, Jones quickly confessed, declaring, according to Marshals Service inspector Barry Golden: "I knew this would catch up with me some day."
If Jones almost shrugged, those who knew him as Keith did not, including his wife, whom he married in 1983. Susan Keith, 56, told police she was in the dark about her husband's crime, incarceration and prison escape.
That she had a murderer for a husband was inevitably shocking. "She had no idea," Tammy Smith, a neighbour, told the Sun Sentinel newspaper. "I talked to her. She's extremely distraught."
The home of James Robert Jones in Deerfield Beach, Florida. Photo / AP
Joe Onischuk, who lives across the street, told the Associated Press news agency: "They are nice people. That's what I don't understand. I couldn't understand that he ever got involved with something like that. I just can't believe it."
The ignorance on the street - even in the marital bedroom - of Jones's true identify seems to have been total. No one knew he had been in the military, let alone that he was convicted in 1974 of stabbing to death a soldier named Lonnie Easton, then 18, while stationed at the former Fort Dix in New Jersey.
Jones is now back behind bars in Fort Lauderdale county jail, awaiting transfer to US military authorities who will probably transfer him back to Leavenworth at least to serve out the remaining 20 years of his original sentence, if not more.
He will find the jail a bit different. The old brick-and-stone fortress, often called "The Castle" for its forbidding architecture, that he escaped from has since been demolished and replaced with a new facility with more humane conditions but perhaps more escape-proof security.
Just how Jones pulled off his vanishing act we have yet to find out. Eleven prisoners made it out of the Castle between 1977 and 1998 - it closed four years later - but all except Jones were recaptured. There is almost no one still around who can recall the details of his breakout. "We don't have access to that," Mr Golden said. "It must have been something elaborate, because he got away and he disappeared."
Where he disappeared to we do now know. With its easygoing ways, warm climate and large community of drifters and bums looking for a break, the Sunshine State must have seemed the obvious place to head to; in hindsight, he might wish he had travelled beyond US shores.
What he did take care to do was never to get in trouble with the law. Jones was for all that time on the US Army's most-wanted list, and one fingerprinting down at the police station would have done him in.
"This guy really lived a normal life," Mr Golden added. "He was basically off the radar. He probably assumed someone else's identity."
- UK Independent