Separately, traces of McGill’s semen were also found on the grandmother’s green dress.
But Det Supt McCubbin, who has now retired, told the documentary the forensic evidence alone was not enough to secure a conviction.
He said: “It didn’t matter what DNA we had.
“He’s got the perfect alibi. How could he commit the murder if he was in prison?”
Records were hard to find as HMP Edinburgh had been rebuilt at the time of the murder and, in an era before computers, paperwork had been lost.
Mr McCubbin’s quest eventually took him to the National Records of Scotland, in the heart of Edinburgh, where he tracked down the governor’s journals.
And a single entry changed everything.
Next to a prison number was the name “G McGill” and the acronym “TFF”.
Mr McCubbin said: “That was Training For Freedom, which meant weekend home leave.”
The inquiry team discovered McGill was on two days weekend leave, with three days pre-parole leave added on, and returned to the prison on 27 September 1984.
Former senior investigating officer Mark Henderson said: “That was the golden nugget we were looking for.”
McGill was finally arrested on 4 December 2019 .
At the time he was still being managed as a sex offender, but was working in the Glasgow area as a fabricator for a company based in Linwood, Renfrewshire.
Gina said the news came as a relief and added: “I never thought I would see it in my lifetime.”
McGill finally was found guilty after a four-day trial in April 2021 and jailed for a minimum of 14 years.
The judge, Lord Burns, told the High Court in Glasgow that McGill was 22 when he strangled Mary but stood in the dock as a 59-year-old.
He added: “Her family has had to wait all that time in order to discover who was responsible for that act knowing that whoever did it was probably at large in the community.
“They had never given up the hope that someday they would find out what had happened to her.”
