By the time they arrived at a small watchmaking school in this town south of Wilmington, Del., the nine military veterans had taken some hard knocks. Some had knee or back injuries from wear and tear, or ringing in the ears from the roar of plane engines. Some struggled with P.T.S.D., a legacy of gunfire, explosions or other trauma.

Leaving the military had presented its own challenges. In interviews, several of the students described feeling lost and lacking purpose, unsure about what they wanted to do next — or what their bodies would let them do — and how they could best fit into the civilian world.

Then, in one way or another, they learned about the Veterans Watchmaker Initiative (V.W.I), a not-for-profit organization that since 2017 has offered honorably discharged veterans tuition-free training in an old-school skill that is very much in demand.

“It’s like being given a second chance at life,” said Zachary Scoular, who left the U.S. Marine Corps last year after eight years of service and, at 27, is the youngest member of the class.

The students had come from all over the country, span more than 30 years in age and served in four different branches of the military. To earn a spot, each veteran had to pass aptitude tests and spend six weeks learning to become a quartz watch technician at the school.