One cop who did not turn his back on Mayor Bill de Blasio at Sunday’s police funeral was Pat Lynch, the head of the Patrolman’s Benevolent Association.

Lynch was in dress uniform complete with white gloves and he positioned himself at one end of the color guard outside the Brooklyn funeral home where the service had just come to a conclusion.

Police Commissioner William Bratton and Chief of Department James O’Neill had already done the same at the other end of the color guard.

Moments later, out came the mayor. De Blasio clearly saw Lynch standing there before him. Lynch no doubt saw him. And that would have been the moment for Lynch to turn his back.

But Lynch continued to face forward. And it was likely not because Bratton had put out an eloquent memo asking cops not to confuse grieving with grievance and turn their backs on the mayor at the funeral for Det. Wenjian Liu, as some had the week before at the services for Det. Rafael Ramos as well as at the hospital the day the two officers were assassinated.

Despite Bratton’s request, hundreds of officers had turned their backs when De Blasio appeared on the Jumbotrons outside the Aievoli Funeral Home on Sunday, the time having come for the mayor to deliver a eulogy inside. These officers were acting very much like cops whose union leader, Lynch, had charged that De Blasio had the blood of their murdered comrades on his hands because he had abetted police-haters.

Yet, for all his heated rhetoric and despite having two sons who are cops and therefore in harm’s way, Lynch did not appear even to consider turning his back on De Blasio as they now stood facing each other. Lynch’s shoulders and hips remained as square as those of the color guard.

Lynch was surely not afraid of showing disrespect to the mayor. He must have felt that to turn his back in thes circumstances would be to show disrespect to the murdered cop’s family and to the department’s most sacred ritual.

One question was why Lynch did not think this was also true of cops who turned their backs earlier on Sunday. The long rows where the officers did turn their backs could be seen as just an extension of the color guard that had formed on this same street.

Lynch was surely not signaling that he was anything but completely supportive of the cops who had just turned their backs or that enough was enough. The most likely answer is that Lynch makes a distinction between turning your back to an image on a screen down the street in the midst of the service and doing it in person where the murdered cop’s family would be emerging.

Lynch kept gazing straight ahead as De Blasio joined Bratton at the other end of the color guard. They stood in a single row, united by solemn respect as the Liu family remained inside. The family was taking some private moments for a closing of the coffin in keeping with Chinese ritual.

Lynch, De Blasio, Bratton, and the thousands of cops all joined in observing NYPD ritual by saluting as the flag-covered coffin was then shouldered from the funeral home by an honor guard.

Behind it came Liu’s parents and his widow, Pei Xia Chen. She kept to Chinese tradition by clutching a large stick of incense and a framed photograph of her deceased husband, this of Liu in his NYPD uniform, an American flag in the background.

Twin buglers played “Taps” and three police helicopters flew overhead in the missing-man formation. Chen bowed her head during the playing of “America the Beautiful.”

Toward the end of the funeral, she had delivered a brave and tender eulogy in which she said that her loving and devoted husband would live on in her and his family. She now looked as if too much of her were in the coffin that the honor guard carried to the hearse.

To look at her in tears was to behold the enormity of her loss. And to see that was to wonder why anybody was worried about anything so small as who turned their back on a Jumbotron up the street.

Someone standing beside Chen took the portrait of her husband when a white-gloved captain stepped up to present her with the flag that the honor guard had lifted from the coffin and ceremoniously folded.

Chen stood for a few heartbeats holding the flag with two hands, just as Ramos’ widow had the weekend before. One difference was that Chen was herself wearing white gloves.

The people around Chen seem to be keenly attentive and one of them took careful possession of the flag while she again clutched the portrait of the man she had called her soul mate in the eulogy.

“You are an amazing man,” Chen had said directly to him.

Chen carried the portrait with her to the pair of black limousines that stood waiting for her and her husband’s parents. The father, Wei Tang Liu, had also delivered a eulogy. He had spoken of an only child who was a No. 1 son in every way. The father had labored in a garment factory when the family first came to America on Christmas Eve 1994 and he recalled his son coming after school to help him finish the work. That same desire to help had led his son to become a cop after the 9/11 attacks and for seven years he had he had called his father at the end of every tour.

“He called me every day before he finished work, to assure me that he is safe, and to tell me: ‘Dad, I’m coming home today. You can stop worrying now,’” the father told the mourners.

No call had come on Dec. 20, four days before the 20^th anniversary of the family’s arrival in America. The father now joined his wife and his son’s widow in the limousines marked with the word “Family” in English and Chinese.

Other relatives and friends climbed into vans. Buses filled with cops from the 84th Precinct, where Liu had worked. He had often been assigned to the Brooklyn Bridge, and he likely encountered protesters who called him and his fellow cops murderers and racists.

RELATED: NYPD Salutes Murdered Officer Wenjian Liu (Photos)

Police motorcycles rumbled past. The NYPD Emerald Society Pipes and Drums struck up a slow march, leading the hearse and the limousines and the rest of the procession down a broad stretch of 65^th Street lined with thousands upon thousands of officers. They included the officers who had turned their backs on the Jumbotron, but there now was only reverence in their ranks.

Beyond the huge American flag that hung over the street, the mile-long mass of cops ended. The procession continued on to the Cypress Hill Cemetery, where Ramos was buried the week before.

“Partners for eternity,” Bratton had called Liu and Ramos.

The band turned back around, raising a lively tune to signal life would go on.

“Stay in formation,” a sergeant from the ceremonial unit said over a public address system to the cops along the street.

The band was still on its way back as De Blasio and his wife departed. Bratton remained at one end of the color guard, Lynch at the other until the band arrived back and the sergeant on the pubic address system formally announced the end of the ceremony, thanking everyone “on behalf of the mayor and the police commissioner.”

Bratton headed off to a waiting car. He no doubt had heard by then that some of the cops had ignored his request and turned their backs. He was also no doubt disappointed.

Lynch stayed in the street, exchanging greetings with cops who had been in formation and were now streaming past. He called them “brother” with clearly genuine affection.

Lynch had seemed a touch uneasy when he took the position beside the color guard and some cops had said that he would normally have been expected to stand with the leaders of the other police unions and the politicians. He insisted he had only been in keeping with tradition.

“We got away from that for a while,” he said.

Whatever the historical precedent and whatever his reasons, Lynch had placed himself in one spot where even the most angry cops could not have expected him to turn his back.

The result was a time, however brief, when Lynch and De Blasio and Bratton stood in a row bound by a shared, if not mutual respect.

And in that there seemed to be hope.

Some observers have expressed fears that the city’s safety may be at stake in this clash between the cops and the mayor, as the cops seem to have also been turning their backs on low-level violations.

More knowledgeable people note that the vaunted “broken windows” theory was never really at the core of the strategies that transformed New York into the safest big city in America.

The actual guiding principle was essentially that black lives matter, that crime had to be addressed as seriously in poor neighborhoods as it was in rich ones.

Even so, a dispirited police force cannot be expected to continue producing such seeming miracles as this year’s record low in murders even as stop-and-frisk was drastically curtailed.

That was accomplished by cops such as the one whose picture was clutched so tightly by his widow on Sunday. Liu’s memory remains as a rebuke to all those who condemn cops as a group and a guide for fellow officers who strive to follow a righteous path. A banner that had hung by Liu’s coffin in the funeral parlor so rightly said this in Chinese:

“A model for all police.”