AIRBORNE CONFLICT BETWEEN CORP-SMT ON CROSS OVER TO OPPOSITE RWY AND ACR-LGT ON STRAIGHT IN APCH.

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I ARRIVED AT THE ARPT (ONY) AT XA30 AND BEGAN PREPARING FOR THE XB00 DEP. WE DEPARTED SHORTLY AFTER XB00; FLEW 30 MINS TO THE FIRST DEST (SEP) AND THEN 40 MINS TO THE SECOND DEST (DAL); ARRIVING AT APPROX XC30. WE WAITED UNTIL XH45 TO DEPART FOR HOME (ONY). THERE WE WAITED UNTIL XN15 AND DEPARTED FOR DAL. ONCE THERE; WE PICKED UP 7 PAX AND DEPARTED DAL AT APPROX XO30 FOR ONY. ONCE AT ONY WE DROPPED OFF 6 PAX AND THEN LEFT AT XP25 TO TAKE 1 PAS TO SEP ARRIVING AT XQ00. FROM THERE WE DEPARTED VFR TO GO BACK TO DAL AND PICK UP THE LAST PAS AND TAKE HIM TO ONY. IT WAS ON THIS LEG OF THE FLT THAT THE INCIDENT OCCURRED. WE WERE AT 2000' ON A RIGHT DOWNWIND FOR RWY 13L TALKING TO THE FINAL APCH CTLR. THE CTLR INFORMED US THAT THERE WAS AN LGT ON FINAL FOR RWY 13R AND WE WERE TO REMAIN ON DOWNWIND UNTIL THE LGT PASSED OFF OUR RIGHT AND THEN WERE TO TURN RIGHT BASE BEHIND HIM FOR THE LEFT RWY. THE ACFT THAT I SAW AT OUR 11 O'CLOCK WAS THE LGT. HOWEVER; AT THE TIME; IT LOOKED TO ME THAT IT WAS FARTHER OUT THAN THE CTLR HAD STATED AND I OBSERVED ANOTHER ACFT ON SHORT FINAL FOR RWY 13R. SEEING THE CLOSER ACFT OFF OUR RIGHT I BEGAN OUR TURN TO BASE. IT WAS THEN THAT THE CTLR INFORMED ME THAT I HAD INDEED TURNED IN FRONT OF THE LGT AND STATED THEIR ALT AT 1300' DSNDING ON FINAL. I STATED TO THE CTLR THAT APPARENTLY I OBSERVED THE WRONG AIRPLANE. I WAS STILL AT 2000' WHEN I CROSSED THE LGT'S APCH PATH. THE CTLR TOLD US TO CONTINUE AND TO CONTACT THE TWR. WE CROSSED IN FRONT OF THE LGT BY APPROX 1/4 MI AND DID NOT START OUR DSCNT UNTIL ON FINAL FOR RWY 13L. AT THAT TIME I HAD BEEN ON THE JOB FOR SOME 17 HRS AND HAD FLOWN FOR 3.8 HRS. NOT HAVING HAD ANY SLEEP OR REST SINCE XZ00 THAT MORNING; I WAS VERY TIRED AND MY JUDGEMENT AND DECISION MAKING ABILITY WAS IMPAIRED. BEING ON THE JOB FOR MORE THAN 14 HRS WILL TIRE ANYONE. HOWEVER; TRYING TO EXPLAIN TO A BUSINESSMAN WHO WORKS 14-16 HRS DAILY ALL HIS LIFE THAT YOU CANNOT FLY AFTER 14 DUTY HRS IS IMPOSSIBLE. IN HIS OPINION; IF YOU ARE NOT READY TO GO 24 HRS A DAY YOU ARE NOT READY TO WORK AT ALL. I KNOW WHY WE HAVE REGS AND I UNDERSTAND THEIR IMPORTANCE. MY EMPLOYER; HOWEVER; HAS NO REGARD FOR THEM. TO HIM THEY ARE A HINDERANCE AND ARE MADE FOR THE 'OTHER GUY.' FROM NOW ON I WILL HAVE A SOLUTION FOR THE PROB: WE NOT HAVE 2 OTHER PLTS ON OUR INSURANCE AND THEY WILL GET TO EXERCISE THEIR PILOTING PRIVILEGES SHOULD THIS EVER OCCUR AGAIN.