Chapter 7 of the JFK 7110.67H SOP. I remember on a show about JFK I have taped from probably 8 years ago. They showed a DHL DC-8 that called a 33 and they explained the emergency process at Kennedy.
7-8 EMERGENCIES
a. On a CALL 33, advise the pilot prior to landing, that the emergency
equipment is standing by.
b. On a CALL 32, advise the pilot prior to landing, that the emergency
equipment is standing by as a precautionary measure.
c. On a CALL 32 or 33, after the aircraft has landed without apparent difficulty,
ask if there is any further need for the emergency equipment, and advise Ground Control
accordingly.
d. When emergency vehicles are responding to an emergency call, the Local
Controller shall approve requests by Ground Control to cross active runways with
emergency vehicles without delay. If necessary, departures shall be held, and arrivals
shall be sent around in order to accommodate the crossing of runways by emergency
vehicles. If emergency vehicles receive approval to enter an active runway, Car
100/99/98 will advise when the runway is subsequently clear of vehicles.