HDG TRACK POS DEV IN RADAR VECTORING FOR IAP ILS APCH. POTENTIAL CONFLICT ALERT FROM TCASII TA.

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WHILE ON A 10 MI BASE TO FINAL FOR RWY 18R AT DFW ARPT; OUR TCASII GAVE US A 'TFC; TFC' ALERT FOR AN ACFT INDICATING 800 FT BELOW US IN A CLB AT OUR APPROX 12 - 1 O'CLOCK POS FOR 3 MI. WE ASKED THE APCH CTLR IF HE HAD THE TFC. HE RESPONDED YES THERE WAS VFR TFC AT 2500 FT (500 FT BELOW US) AND TOLD US TO TURN R TO 150 DEGS; CLRED THE ILS RWY 18R APCH AND SWITCH TO TWR FREQ. AT THIS POINT THE TCASII GAVE US AN RA TO 'MONITOR VERT SPD.' WE FOLLOWED THE TCASII COMMAND ENSURING WE DID NOT DSND AND ATTEMPTED TO VISUALLY ACQUIRE THE TFC THROUGH THE BROKEN CLOUDS. THE TCASII SOON GAVE US A CLR OF CONFLICT AURAL SIGNAL. WE THEN NOTICED WE HAD GONE THROUGH THE LOC COURSE AND IMMEDIATELY TURNED TO A 200 DEG HDG TO CORRECT. TWR THEN CALLED US AND TOLD US TO TURN TO A 200 DEG HDG IMMEDIATELY. WE RESPONDED THAT WE ALREADY HAD. THE REST OF THE APCH AND LNDG WAS UNEVENTFUL. I FEEL IF THE APCH CTLR HAD GIVEN US AN EARLIER TA WE WOULD NOT HAVE BEEN OVERLOADED BY RESPONDING TO AN RA; TRYING TO FIND THE TFC; INTERCEPT FINAL AND SWITCH TO THE TWR FREQ.