Large Transport; Low Wing; 2 Turbojet Eng
Maintenance Airframe; Maintenance Powerplant
Maintenance Technician 8
Communication Breakdown; Situational Awareness
Deviation / Discrepancy - Procedural Clearance; Ground Incursion Runway
Flight Crew Returned To Clearance
Aircraft; Human Factors; Procedure
I was instructed to move under tow Aircraft X from November to Hangar 3S.  A super tug was connected to Aircraft X to move the aircraft.  It was not a taxi.  When holding short of Victor on Alpha; I was instructed by ATC Ground 121.90 to go left Uniform hold short Runway 13L.  The tug has a slow top speed.  On the way to Uniform; ATC instructs Aircraft X to Cross Runway 13L; 'Aircraft X without delay cross Runway 13L traffic 4 miles final.'  I was on Uniform approaching Uniform-Alpha when the directions were said.  I took this as a new set of instructions and proceeded to the next available taxiway to cross Runway 13L.  We moved the aircraft across Uniform-Alpha then Left Charlie-Bravo to Charlie. ATC said the whole 'taxi' was unacceptable and to call the ATC Tower.  I called the Tower and then explained the situation.  About 3 hours later the Port Authority Airport spoke to me and issued me a BOR for a runway incursion and pulled my Port ID.  The ATC Controller needs to specify what taxiway to cross the runway.  When ATC called and advised to cross Runway 13L without delay; it sounded like a whole new set of instructions and the ATC assumed I was already at Uniform.  This was not the case and I was nowhere near Uniform.  The aircraft was under tow with a slow tug and I would've never made it to Uniform and then cross 13L with traffic 4 miles final.
JFK tow driver describes a situation where he is using a slow tug to move an aircraft across a runway.  JFK Controller tells tug driver a new instruction; driver crosses runway and then later is issued a 'ticket' and his ID is pulled.