LGT OVERSHOT RWY CTRLINE WITH PARALLEL APCHS IN PROGRESS.

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ON RADAR VECTORS TO INTERCEPT RWY 24R AT LAX. HVY SMOG AND THICK HAZE; BAD VISIBILITY TO W. FLT TEST PROCS OCCURRING BTWN CAPT AND SO THROUGHOUT ENTIRE FLT. (I WAS PUT ON THIS WITH NO FLT TEST TRAINING AND AGAINST MY WILL.) CONSTANT CHATTER BTWN THESE GUYS BELOW 10000 FT VERY DISTRACTING. ON BASE INTENSE CONVERSATION ABOUT MALFUNCTIONING NOSE GEAR IN TRANSIT LIGHT ERUPTED. APPARENTLY IN THE MIDDLE OF ALL THIS THE CAPT TOLD APCH WE HAD THE RWY. HE NEVER ASKED ME IF I HAD IT; SO I CONTINUED ON RADAR VECTORS. I DON'T KNOW IF WE WERE REALLY CLRED FOR A VISUAL OR NOT. IF WE WERE; I NEVER HEARD IT BECAUSE OF THE ENGINEER'S CONSTANT BLABBING ABOUT THE NOSE GEAR LIGHT. APPARENTLY WHAT THE CAPT WAS LOOKING AT WAS THE S LAX COMPLEX; RWY 25L/R WHICH IS FURTHER W THAN THE 24 N COMPLEX. I COMPLAINED THAT ATC SHOULD HAVE TURNED US BY NOW OR CLRED US FOR THE ILS. THE CAPT JUST SAT THERE AND SAID NOTHING. I INITIATED A TURN BECAUSE I DIDN'T WANT TO GO TO MEXICO! ATC THEN INFORMED US WE WERE WELL S OF COURSE. WITH PARALLEL APCHS IN PROGRESS THIS WAS A DANGEROUS SIT. NEITHER OF US EVER HAD RWY 24L OR RWY 24R IN SIGHT AT ANY TIME DURING THIS PHASE OF APCH. I FEEL IT IS INEXCUSABLE FOR THE PNF TO CALL THE RWY IN SIGHT WITHOUT ASKING THE PF IF HE HAS IT OR NOT.