CREW TAXIING LGT CARGOLINER GOT CONFUSED AND CROSSED ACTIVE RWY 18L WITHOUT CLRNC. RWY INCURSION.

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ACFT WAS ORIGINALLY CLRED TO LAND ON RWY 18R. DUE TO DISABLED ACFT ON RWY; LNDG CLRNC WAS REISSUED; AND WE WERE CLRED TO SIDESTEP TO RWY 18L AND CLRED TO LAND. AFTER LNDG TWR CLRED US TO TAXI TO OUR RAMP. WE ASKED TWR IF WE COULD TURN R ONTO RWY 9/27; THEN USE TXWY C; AND TXWY J TO TXWY. CAPT TURNED R ON TXWY C; THEN TURNED L ON TXWY N. CAPT THOUGHT HE WAS ON TXWY J. ACFT CAME TO A STOP AT THE END OF TXWY N. THAT'S WHEN CAPT REALIZED HE WAS ON WRONG TXWY. TWR THEN CLRED US TO TURN L ONTO RWY 9/27; TAXI BACK TO TXWY C; GO TO TXWY B; TURN L; THEN TAKE TXWY W. UPON ENTERING RWY 9/27; CAPT BEGAN A FASTER THAN NORMAL TAXI SPD. I (FO) TOLD CAPT NOT TO MISS TXWY C; THAT IT WAS COMING UP AND PRIOR TO RWY 18L. AFTER I LOOKED UP FROM TXWY ARPT DIAGRAM; CAPT HAD ALREADY PASSED TXWY C; AND WAS XING RWY 18L. CAPT WAS OBVIOUSLY DISORIENTED AS TO HIS POS AND THAT OF TXWY C. ACFT CROSSED RWY 18L WITHOUT CLRNC; TWR THEN GAVE A PROGRESSIVE TO THE RAMP. CAPT SHOULD NOT HAVE TAXIED AS FAST AS HE WAS; AND WHEN HE REALIZED THAT HE WAS DISORIENTED WITH RELATION TO HIS POS ON GND; HE SHOULD HAVE STOPPED ACFT IMMEDIATELY. ALSO; HE COULD HAVE USED HIS CREW MEMBER'S INSTRUCTIONS; BUT ELECTED TO DISREGARD THEM. IN ANY EVENT A RWY INCURSION DID TAKE PLACE UPON RWY 18L FROM THE INTXN OF RWY 9/27 AT TPA ARPT. NO LOSS OF SEPARATION EVER OCCURRED.