FLC OF AN A300-600 BECAME DISORIENTED DURING TAXI FOR TKOF AND MADE THE WRONG TURN TO ANOTHER TXWY THAN THAT ASSIGNED. THE TWR CTLR NOTICED THEIR MISTAKE AND ISSUED NEW INSTRUCTIONS FROM THAT POINT WHICH PREVENTED AN ACCIDENTAL INCURSION OF THE ACTIVE RWY.

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REFER TO 10-9; CLE; OH; FOR REF. OUR TAXI CLRNC FROM CARGO RAMP WAS TO RWY 23L VIA TXWY J (N); ONTO PAX APRON TO TXWY W; THEN RWY 28 TO HOLD SHORT OF RWY 23L. DUE TO MANY CLOSED TXWYS AND POOR MARKINGS; WE MANAGED TO MISTAKE RWY 23L FOR RWY 28 AT N POINT OF TXWYS J; L; AND W. WE STARTED TO TURN L ONTO TXWY W AND ASKED ATC TO CLARIFY THAT WE WERE CLRED ONTO RWY 28. (TWR CTLR WAS WORKING ALL FREQS -- TWR; GND; CLRNC.) CTLR VERIFIED WE WERE CLRED ONTO RWY 28; HE SAW OUR ERROR TURNING E VICE W AND CLRED US ONTO RWY 23L AT TXWY W FOR TKOF OR BACK TAXI FOR TKOF FULL LENGTH. HE SAVED US FROM AN INCURSION! BOTH OF US (2 MAN ACFT) HAVE BEEN IN/OUT OF CLE BEFORE; AND WE HAD DISCUSSED THE TAXI RTE AT LENGTH PRIOR TO PUSHBACK. WE STILL GOT TURNED AROUND APCHING THE SPOKE- LIKE INTXN OF TXWYS J; L; W. PART OF THE PROB WAS CONSTRUCTION AND THE OTHER WAS HUMAN ERROR. I DO BELIEVE THAT NOTAMS COULD HAVE BEEN MORE ACCURATE AND THAT OUR COMPANY DIAGRAM MORE DETAILED TO TXWY CONFUSION POINTS. OUR REQUEST FOR ROUTING CLARIFICATION; THOUGH THE CTLR WAS BUSY WORKING 3 FREQS; PREVENTED AN INCURSION. I HIGHLY RECOMMEND CLARIFYING ANY CLRNC TO CROSS ANY ACTIVE RWY. WHEN IN DOUBT -- CALL.