AN ACR B767 FLC; AT THE END OF A LONG FLT AND APCHING INTO THE SETTING SUN; GETS SEVERAL RWY CHANGES; AN RA TO CLB; THEN OVERSHOOTS RWY 24L TOWARD THE RWY 25 COMPLEX WHILE LOOKING FOR TFC AND MISIDENTING THE RWY. THE FLC CORRECTS AND THE TWR CHANGES THE RWY AGAIN TO RWY 24R. LNDG SUCCESSFUL.

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OUR FLT WAS A LONDON TO LAX FLT ON R DOWNWIND FOR LAX RWY 24R AFTER 10 HRS 15 MINS FLYING TIME. TIME XA10L; NO CEILING. BUT HAZE WITH SUN IN THE LOWER WESTERN QUADRANT. SOCAL GAVE US A TURN TO 170 DEGS FOR BASE RWY 24R. AT THE SAME TIME WE GOT A TCASII RA TO CLB (I BELIEVE). CAPT MADE MANEUVER TO FOLLOW TCASII. SOCAL SAID TFC NO PROB. TCASII GAVE CLR OF CONFLICT. SOCAL CALLED 11 O'CLOCK TFC FOR RWY 25L AND CHANGES LNDG RWY TO 24L. CAPT LOOKED INTO HAZE; NOW SAYS HE HAS RWY 24L IN SIGHT AND SOCAL CLRED FOR VISUAL RWY 24L AND CONTACT TWR. CAPT WAS LOOKING AT RWY 25 COMPLEX WHEN HE SAYS HE HAD RWY 24L (BECAUSE HE WAS LOOKING INTO SUN). TWR CALLED TFC FOR RWY 25L; HAD US IN SIGHT. CAPT OVERSHOT RWY 24L CTRLINE TO THE S AND FO CALLED FOR CORRECTION BACK TO CTRLINE. CAPT NOTICED OVERSHOOT AND CORRECTED. TWR NOW CHANGES RWY TO RWY 24R AGAIN. RWY 25L TFC STILL HAD US IN SIGHT. LNDG RWY 24R NORMAL. DURING OVERSHOOT I WAS OUTSIDE LOOKING FOR RWY 25L TFC. OTHER CREW MEMBERS ALSO LOOKED FOR RWY 25L TFC DURING OVERSHOOT. CAUSE: DISTR FROM TCASII RA TURNING DOWNWIND TO BASE WHILE SOCAL CALLED OUT RWY 25L TFC. PERCEPTION THAT RWY THAT WAS IN SIGHT AND GLISTENING FROM SUN REFLECTION WAS THE CORRECT RWY WHILE CORRECT RWY WAS IN HAZE SHADOWS. MULTIPLE RWY CHANGES ON BASE; FINAL CIRCUIT. POSSIBLE FATIGUE DUE TO 10 HR 30 MIN FLT TIME AND INADEQUATE B767 CREW REST FACILITIES. MULTIPLE DISTR; TFC CALLOUT AND RWY CHANGES. RECOMMEND: ON HAZY DAYS WITH REDUCED VISIBILITY; MAYBE RADAR VECTORS TO FINAL (AT LEAST AT LAX WITH MULTIPLE RWYS) SHOULD BE STANDARD PROC.