Surprised by reports that workers are toiling — or “toiling” — around the clock to rack up close to $1.4 billion in annual overtime, the Metropolitan Transportation Authority convened an emergency meeting late Friday to figure out why.

The only thing figured out was that even on matters of fraud or dangerous behavior, the MTA’s ­labor unions won’t cooperate with their ally Gov. Andrew Cuomo, if it means imperiling extra pay.

The MTA board met just as Cuomo called the hours clocked by several Long Island Rail Road workers “physically impossible.” At the meeting, Cuomo appointee Larry Schwartz observed, “I don’t think any human being of sound mind and body would ever believe that somebody could work 3,800 hours of overtime in a single year.”

That’s 73 extra hours a week: the hours reported by now-retired LIRR maintenance employee Thomas Caputo to take home nearly half a million dollars, ­according to the Empire Center.

Schwartz wants the MTA to hire a prosecutor to probe abuse and fraud. Yet it isn’t clear why the MTA can’t do this in-house: It has a whole anti-fraud department.

LIRR unions should want a probe. Either some workers are stealing, harming their colleagues or they’re working so much that they’re putting safety at risk.

As MTA Chairman Pat Foye pointed out, federal investigators are still looking into why an LIRR track foreman died in 2017. “The deceased LIRR foreman had been on duty for 11 hours with 13 hours remaining . . . and had worked 64.45 hours in the days prior to the fatal incident,” Foye said. He also noted that people who have supposedly worked around the clock drive their personal cars home on Long Island’s roads, where they put others in danger.

The board’s sudden interest in how its workforce actually does its work is welcome — but the risk is that the MTA is tempted to make an example of what another Cuomo board member, Kevin Law, called “bad apples sleeping on the job.”

It’s hard to blame workers for taking expert advantage of bad management. As Schwartz pointed out, the LIRR often posts weekend work assignments for 55 or 48 hours of straight-through work. “I don’t know any human being, including myself, who can work 55 hours straight in a weekend,” he said.

And work rules enshrined in decades-old contracts allow senior workers to grab the best overtime — meaning the highest-paid workers are working the most, with their extra pay reflected for decades in their pensions.

The MTA doesn’t have an overtime crisis, then, but a work-rule and management crisis, and one that’s most acute at the LIRR. Overtime at the subway and bus division at least has a (mostly) reasonable explanation: The “subway action plan” to repair and replace tracks and signals was at its peak last year.

What the MTA needs most immediately is better LIRR contracts. Nearly two hours into the hearing, Foye said that unless the federal government acts soon to cap hours on safety grounds — a good idea — any caps on overtime “would be the subject of . . . collective bargaining.”

How’s that going to go? Judging from union comments at the meeting, not well. Vincent Tessitore Jr., a United Transportation Union rep for LIRR workers, said the board scrutiny “sickened” him. He added that overtime allocation is a “contractual right,” implying that little will be given up without something in return.

As for the Transport Workers Union, the MTA’s biggest labor force, representing subway and bus workers? It’s a mystery why the TWU cares about protecting rules at the LIRR — rules that are far more generous than what city workers get.

But by declaring an all-out MTA-wide crisis, and even briefly threatening to deploy police to monitor workers’ hours, the MTA has encouraged labor solidarity. “This is the kind of behavior that triggers strikes,” the TWU’s John Samuelsen said.

The MTA can deploy investigators to pore over a few overtime kings’ Facebook pages and travel schedules to, as Cuomo said, “get to the bottom” of “fraud.” But fixing the deeper problem means taking away pay and benefits that railroad workers don’t consider fraud or abuse, but an entitlement that comes with the job.

As Norman Brown, another railroad union veteran on the board, said, the only way to change the status quo is “you negotiate it” — historically impossible to do in riders’ favor without a governor who’s willing to take a strike.

Nicole Gelinas is a contributing editor of City Journal.