FO OF A WDB OVERSHOT TURN TO FINAL DURING VISUAL APCH RESULTING IN A TCASII RA.

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ON APCH TO LAX RWY 24R; WE WERE CLRED TO DSND FROM 7000 FT TO 2500 FT ON HDG 160 DEGS (VECTORS TO ILS; BASE LEG). GOOD VMC. WHILE ON BASE LEG AND DSNDING; I NOTED THE LEADING EDGE FLAP AMBER LIGHT ILLUMINATED. I ASKED THE CAPT AND SO TO VERIFY THE LIGHT AND CHK THE SO PANEL FOR FLAP INDICATIONS. APCH CTL ASKED IF WE HAD LAX IN SIGHT; WE ACKNOWLEDGED; AND RECEIVED CLRNC FOR A VISUAL APCH TO RWY 24R; SWITCH TO TWR. SO RPTED REAR PANEL INDICATED #3 SET OF LEADING EDGE FLAPS WERE STILL UP. WITH 'FLAPS 10 DEGS' POS ON TRAILING EDGE FLAPS; ALL LEADING EDGE FLAPS SHOULD BE DOWN (B-747/2). CAPT THEN POINTED TO THE ALTERNATE FLAP POS SWITCHES; LOCATED OVER MY HEAD. THE ALTERNATE FLAP SWITCH WAS 'ARMED' WITH #3 SET OF LEADING EDGE FLAPS SELECTED 'UP.' CAPT STATED THAT DURING CRUISE (9 PLUS HR FLT; KIX-LAX) THE AMBER LIGHT 'IN TRANSIT' LEADING EDGE FLAPS ILLUMINATED; AND THE CREW ON DUTY (I WAS OFF DUTY) ARMED THE ALTERNATE FLAP SYS AND SELECTED #3 LEADING EDGE FLAPS TO 'UP' WHICH EXTINGUISHED THE AMBER 'LEADING EDGE FLAP' LIGHT. AS SO BEGAN TO LOWER #3 LEADING EDGE FLAPS; I NOTED TFC OUT OF THE CAPT'S SIDE WINDOW (10:30 POS) HDG INBOUND TO LAX FOR RWY 25L. I IMMEDIATELY BEGAN MY TURN TO FINAL FOR RWY 24R AS TWR CALLED THE TFC TO US 'AT 10 O'CLOCK; 1 MI FOR RWY 25L.' MY TURN RESULTED IN A SLIGHT OVERSHOOT OF RWY 24R CTRLINE; BUT NO FURTHER S THAN RWY 24L AT ANY TIME. DUE TO THE CONVERGING VECTOR TCASII TA ALSO SOUNDED FOLLOWED BY 'DECREASE DSCNT.' TCASII ADVISORIES CAME ON DURING MY TURN. TFC WAS ALWAYS IN VISUAL CONTACT; SLIGHTLY LOWER THAN OUR ALT; AND I DID DECREASE MY RATE OF DSCNT TO 300 FPM. 'CLR OF CONFLICT' CALL WAS GIVEN WHEN ROLLING OUT OF TURN ON FINAL COURSE. WE WERE ALL DISTRACTED BY THE AMBER LEADING EDGE FLAP INDICATION; WHILE ON THE 160 DEG HDG/BASE LEG. I ATTRIBUTE THE SLOW RESPONSE TIME TO CREW FATIGUE (9 PLUS HRS ALL NIGHT FLT JAPAN TO UNITED STATES). THOUGH WE WERE ALWAYS VMC WITH ARPT IN SIGHT; THE TURN TO FINAL WAS DELAYED WHILE ATTN WAS DIRECTED INSIDE THE COCKPIT. ALTHOUGH THE TFC CONFLICT WAS GENERATED; NO RADICAL AVOIDANCE MANEUVERS WERE REQUIRED NOR CONDUCTED; SINCE RESOLUTION WAS OBTAINED BY COMPLETING THE TURN TO FINAL. A CONTRIBUTING FACTOR WAS THAT I WAS NOT BRIEFED; UPON RETURNING TO DUTY; OF ANY ABNORMALITY CONCERNING THE FLAPS BY THE OFF-GOING PLT. THE CAPT AND SO WERE BOTH ON DUTY WHEN THE CRUISE AMBER LIGHT ILLUMINATED. NO ONE MENTIONED THIS UNTIL I CALLED THE AMBER LIGHT ILLUMINATED ON BASE LEG.