SMT NON ADHERENCE TO ATC INSTRUCTIONS TFC PATTERN ENTRY HAD NMAC WITH ACR X TCASII CLB. EVASIVE ACTION TAKEN. SEE AND AVOID CONCEPT.

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ACR X CLRED FOR APCH AND LNDG AT HOU RWY 12R USING THE ILS FOR GUIDANCE. FO FLYING. TWR ADVISED US OF TFC ON SHORT FINAL TO RWY 12L (RPTED AS NO FACTOR) AND PARALLEL TFC INTERCEPTING FINAL TO RWY 12L ABEAM AND BELOW US WHO RPTEDLY HAD US IN SIGHT. MUCH OF OUR ATTN CONCENTRATED ON ACQUIRING THIS ABEAM TFC VISUALLY; AS TCASII DISPLAYED THE TARGET IN CLOSE PROX AND PROGRESSING FROM 9:30 TO 8:30 AND 300-100 FT BELOW US. WE FAVORED THE R SIDE OF THE LOC AND DECREASED DSCNT RATE TO PROVIDE SEPARATION AND ASSIST IN ACQUISITION. VISUAL ON THIS TFC WAS NEVER OBTAINED. INSIDE OM AT APPROX 1100 FT MSL WE SUDDENLY GOT A TCASII TA FOLLOWED ALMOST IMMEDIATELY BY AN RA. MY FIRST THOUGHT WAS TO SELECT TA ONLY AND CANCEL THIS 'NUISANCE RA.' HOWEVER; THE TCASII RA WAS FOR TFC LOW AND ON THE NOSE; NOT THE PREVIOUSLY ISSUED TFC. AT THE INITIAL 'MONITOR VERT SPD' ADVISORY; I SAW TFC BRIEFLY AT 12:15 LOW AND WITHIN A MI. TCASII THEN COMMANDED A CLB AND I CAME INSIDE TO CHK THE TCASII WHICH NOW DISPLAYED A 2000 FPM CLB REQUIREMENT. I DID NOT SEE THE TFC AGAIN AS THE CAPT COMMANDED THAT I FOLLOW THE RA. CLB WAS INITIATED SMOOTHLY WITH MAX THRUST. ONLY THE FE SAW THE TFC PASS 100-200 FT BELOW US. THE RA MANEUVER CONTINUED INTO A MISSED APCH WITH VECTORS TO AN UNEVENTFUL LNDG. IN LATER CONVERSATIONS WITH TWR WE WERE TOLD THAT THIS TFC WAS AN SMT THAT HAD BEEN INSTRUCTED TO OVERFLY THE ARPT AND TURN L TO A DOWNWIND FOR RWY 22. INSTEAD THE SMT APPARENTLY TURNED R; DIRECTLY INTO THE RWY 12R APCH COURSE. MY ASSESSMENT WAS THAT THE TCASII DISPLAY WAS ADEQUATE AND THAT THE REDUCED WARNING TIME WAS CAUSED BY THE SUDDEN MANEUVER OF THE OTHER ACFT INTO OUR FLT PATH. SOME PLTS INHIBIT THE RA FUNCTION IN THE TERMINAL AREA; ESPECIALLY FOR ARRS AND DEPS TO/FROM PARALLEL RWYS; AS AUTHORIZED IN OUR FLT HANDBOOK PROCS. I WOULD ENCOURAGE REMAINING IN TA/RA UNTIL A 'NUISANCE RA' IS EVALUATED OR UNTIL SAFETY OF FLT DICTATES OTHERWISE.