ACR WDB FREIGHTER TAXIES ONTO CLOSED TXWY DURING A NIGHT OP. NON ADHERENCE TO ATC INSTRUCTION.

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WE LANDED AT JFK ON RWY 13L; ROLLED TO THE END; AND TURNED OFF R; ONTO YA. TWR DIRECTED US TO MAKE FIRST L. HOWEVER; AT THIS TIME; ACFT WAS ALREADY PAST THE POINT TO MAKE A L TURN ONTO ZB. WE WERE FACED WITH A L TURN ONTO Y OR A 270 DEGS R TURN IN ORDER TO GO DOWN ZB. CAPT ASKED CREW WHICH TAXI TO GO DOWN ZB OR Y (NOT CALLING EACH BY NAME; JUST POINTING). FO SAID LET ME ORIENT MYSELF WITH MAP AS I HAD HAD HEAD DOWN DOING AFTER LNDG DUTIES. SO POINTS TO TXWY TO THE R CHOICE (Y) AND SAYS VERY POSITIVELY AND EMPHATICALLY THAT THAT IS THE CORRECT TXWY TO GO DOWN (POINTING TO Y). CAPT PROCEEDS DOWN Y WITHOUT INPUT FROM FO. AT END OF Y (AT F); PROGRESS IMPEDED DUE TO RUBBER STANCHIONS ACROSS TXWY AND WE REALIZE WE ARE ON THE WRONG TXWY; THAT WE ARE INDEED ON Y AND IT IS CLOSED. WE NOW HAVE NO DOUBT AS TO WHERE WE ARE. WE HAD TO SHUT DOWN AND GET TOWED IN FROM THERE (NO ROOM TO TURN AROUND). CONTRIBUTING FACTORS: CAPT PROCEEDED WITHOUT KNOWING EXACTLY WHERE HE WAS ON ARPT. CAPT UNAWARE A CLOSED TXWY WAS ONE OF THE CHOICES HE WAS LOOKING AT. CAPT ASSUMED TWR CTLR KNEW OF OUR EXACT LOCATION WHEN SHE DIRECTED US TO MAKE NEXT L (OR DID SHE SAY FIRST L -- I AM NOT SURE). I DON'T THINK THIS IS A REASONABLE ASSUMPTION. CAPT PROCEEDED WITHOUT CONSENSUS FROM ENTIRE CREW. THE POSITIVENESS AND EMPHASIS OF SO'S RESPONSE (WAS VERY REASSURING). NO RUBBER STANCHIONS OR ANY MARKINGS ON THE TXWY (Y) AT THE N END (WHERE WE TURNED ONTO IT) TO INDICATE IT WAS CLOSED (LIKE AT THE S END). SUPPLEMENTAL INFO FROM ACN 250818: AFTER COMPLETING A VOR/VISUAL APCH TO RWY 13L; THE GND CTLR GAVE US COMPLEX TAXI INSTRUCTIONS WHILE WE WERE DECELERATING ON THE RWY. WHEN WE WERE CLR OF RWY 13L (AT THE END) WE TAXIED ON TXWY YA AS WE ATTEMPTED TO CLARIFY THE TAXI INSTRUCTIONS. THE GND CTLR TOLD US TO MAKE THE FIRST L. HOWEVER; AT THIS POINT WE HAD PASSED THE INTXN OF YA AND ZB; AND BY MAKING THE L TURN WE FOUND OURSELVES ON Y (A CLOSED TXWY). THERE WAS; HOWEVER; A CONFUSING ARRAY OF STANCHIONS AND RED LIGHTS THAT WE MISTOOK FOR REPAIR BARRIERS. A MORE TIMELY SET OF PROGRESSIVE TAXI INSTRUCTION; AND MORE DILIGENCE BY ALL CREW MEMBERS WOULD HAVE PREVENTED THIS SIT. SUPPLEMENTAL INFO FROM ACN 250819: AFTER LNDG AT JFK FROM ANC; WE RECEIVED TAXI INSTRUCTIONS (SOMEWHAT COMPLEX) WHILE STILL IN LNDG ROLLOUT WHICH WE HAD TO DISREGARD UNTIL OFF RWY.