What do firefighters do? I mean, obviously they fight fires. But stuff isn't always on fire! And you can't train 24/7, can you?
In the UK, as well as fighting fires and dealing with other emergency situations, they train people to be fire wardens and first aiders; do talks for schools and other groups about fire safety and accident prevention in the home; and fit smoke alarms for homes. I only know this as I recently did emergency first aid training with a fire fighter.
It's similar in NYC. Firefighters do everything mentioned above. They also make periodic inspections of apartment buildings.
Fire houses also receive donations for things like food pantries, winter coat drives and toy drives.
To make sure everything works well, the trucks are also taken out for a brief run every day. Usually, the trucks are making a food run. Firehouse recipes are famous in NYC. That's probably the fun part of being a Firefighter.
Most important, when a 911 call comes in that requires an ambulance, the ambulance will come
from the Fire department.
All in all, there's plenty for a Firefighter to do in 'down time'.