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The 11 others found him not guilty of murder.
When asked by the court registrar if it was probable the one person would change their mind, the jury forewoman replied, "no".
All 12 found him guilty of manslaughter.
The decision came in the High Court at Invercargill just after 4.30pm yesterday, after about eight hours of deliberation.
Ms Reedy’s family were visibly upset at the verdict with sobs heard from the gallery.
The jury returned three times to the courtroom yesterday to seek direction from Justice Jan-Marie Doogue.
The first time, about 11.15am, was to tell her they could not reach an agreement.
"You have only been deliberating for about three and a-half hours which is not long in the scheme of jury deliberations, particularly on a case of this importance," she said to them.
"If in an hour or so you find yourselves in the same position, then we’ll get you to indicate that to the court."
She advised if they had any further questions, they should not hesitate to ask.
Another two questions were asked about 1.45pm.
This time jurors were seeking direction on the law, specifically the part of the Crimes Act which outlines whether the defendant was likely to know whether the injury he was inflicting was likely to cause death, and was reckless, whether death was sustained or not.
Justice Doogue referred back to the direction she gave in her closing, when she said it was not sufficient for jurors to conclude that Fallowfield could have known that strangulation of Ms Reedy was likely to cause death, or that the jurors could have known that this was likely or even that any reasonable person would have known it was likely.
"This is important.
"It’s whether Mr Fallowfield had an actual appreciation that there was a real and substantial risk that death would have followed as a result of strangulation and you must stand in his shoes when you answer that question," she said.
The second question was where in the evidence jurors could look to get a better understanding of whether Fallowfield knew his actions were likely to cause Ms Reedy’s death.
Justice Doogue said jurors would need to infer the answers from a logical look at all of the evidence.
"It’s impossible for any one of us to see into another person’s mind."
However, she said inferences or conclusions about murderous intent could be drawn from evidence jurors considered to be relevant that disclosed what a person was saying or doing at the time.
"An inference or conclusion must be logical, rational and not speculative and it must not be a guess," she said.
The third time the jurors returned to the court was about 3.15pm, when they asked if they could deliver a majority decision rather than a unanimous one.
Fallowfield was remanded in custody to appear for sentencing on October 15 this year.