TCASII LOGIC. ACR X TCASII RA FROM Y ISSUES RA CLB THEN DSND. POSSIBLE LTSS.

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APCH CTL GAVE TFC '12 O'CLOCK; 8 MI; 6000 FT' (WE WERE AT 7000 FT). FO SAID 'TFC IN SIGHT;' I DID NOT SEE TFC. APCH IMMEDIATELY TURNED US FROM 230 DEGS TO 180 DEG HDG; 'DSND TO 3000 FT.' I PULLED THRUST LEVERS TO IDLE AND DEPARTED 7000 FT FOR 3000 FT LOOKING FOR TFC. AT ABOUT 6200 FT TCASII RA INDICATED A MAX RATE CLB ALTHOUGH WE WERE DSNDING AT ABOUT 2500 FPM. BY THE TIME I LOOKED AT TCASII; IT WAS IN THE RA 'DSND NOW MONITOR V/S' MODE. BY THEN WE WERE GOING THROUGH 5200 FT AND THE LIGHT TWIN WAS DIRECTLY OVER US AT 6000 FT. WE CONTINUED FOR A VISUAL APCH AND LNDG ON RWY 10. AS SOON AS THE FO AND I DISAGREED ON SEEING THE OTHER ACFT. I SHOULD HAVE SPOKEN UP AND ADVISED APCH CTL. IF I HAD PULLED UP AS TCASII ADVISED IMMEDIATELY; MY REACTION TIME WOULD HAVE PUT US IN CLOSER PROX TO THE OTHER ACFT. MY COMPANY'S PROCEDURE IS TO DO JUST THAT. MY COMPANY ALSO HAS A COMPREHENSIVE 'CREW RESOURCE MGMNT' PROGRAM WHICH; REST ASSURED; I THOROUGHLY REVIEWED THE NEXT MORNING. AS FAR AS TCASII; I WAS VERY SURPRISED AT HOW QUICKLY EVENTS TOOK PLACE -- THE VISUAL AND AURAL CLUES CHANGED VERY RAPIDLY.