John Proctor was just 25 and had been visiting his wife June and baby son at the Mid Ulster Hospital on 14 September 1981 when he was gunned down by the IRA.
On Thursday, 54-year-old Seamus Martin Kearney from Gorteade Road in Swatragh, Co Londonderry, was found guilty of the murder.
Outside court, Johnnie Proctor said it was glad the family could now have some closure and justice.
"I never got to meet my father. It's so sad that I never got to meet the man that brought me into the world," he said.
Kearney had denied murder and possession of the Armalite AR15 assault rifle used in the shooting.
But he was told by Belfast Recorder David McFarland that he was satisfied he was "either the gunman, the driver of the Ford Escort RS200 (getaway car) or an occupant of the car present to provide support for the killing".
DNA found on a cigarette butt recovered from the scene later matched Kearney's DNA profile.
The Belfast Crown Court judge said that he was "satisfied beyond reasonable doubt" that the defendant had smoked the cigarette and then discarded it at or about the time of the shooting.
We've been strong this last 32 years, we've waited patiently and now our day has come. I'm relieved that we have finally got justice.
June McMullin, victim's widow
After the guilty verdict was delivered, the victim's widow June wept, saying: "I can't believe it ... I can't believe it." Other members of the family also comforted each other.
In his full 23-page judgement, Judge McFarland said that those who murdered the reservist had gone out "armed to kill and they executed their plan".
"It is abundantly clear that a number of individuals had murderous intent that evening," he said.
"The number involved was definitely two and possibly more. They must have been aware of the movements of John Proctor and that he would be in the Magherafelt Hospital that evening."
The judge added that he had also considered the roles of those travelling in the car, stating that the gunman was "clearly guilty of murder", as was his driver.
However, he had also considered the position of any other person, and had discounted the possibility that such a person would not have been with the car, or in the carpark, "for an innocent purpose, or a criminal purpose short of intending to kill John Proctor".
He said: "The gunman was there to fire the weapon, the driver of the car was there to remove gunman and the weapon .... and any other occupant of the car would have been there to provide support either for the gunman, the driver or both.
"All the occupants of the car are guilty of murder."
Although Kearney was told that the only sentence for murder was life imprisonment, and while he has yet to hear what the minimum tariff will be, he may only serve two years of the eventual sentence under the terms of the Good Friday Agreement.
I consider that the defendant's undoubted propensity to kill members of the security forces and his failure to given an explanation for the presence of a cigarette smoked by him at the car park adds weight to and supports the prosecution case against him.
Judge David McFarland
It is the second time that Kearney has been convicted of a terrorist gun attack.
In December 1984, he was jailed for the attempted murder of UDR soldiers whose Land Rover came under fire in Swatragh in November 1982 - from the same AR15 rifle used to kill John Proctor.
The reserve constable's widow June said outside Thursday's court sitting that the murder had taken the life "out of all of us as a family".
She added: "I heard the gunshots and I knew it was him. I knew Johnnie was dead because I heard the number of shots they put in him. It wasn't just one shot - they riddled him.
In a statement read out on behalf of the family, the policeman's niece Lorna Torrence said: "The life of John Proctor - although cut short by unjustly acts of a cowardly nature - will be remembered for his kindness, warmth and love for his family and his service in the RUC to maintain peace, law and order, to which he lost his life.
"After all these years of heartache and pain, he will never be forgotten."
She added that the process to seek justice had brought truth, peace and healing, stating: "This is what processes like this allow families to do."