LESS THAN STANDARD SEPARATION BETWEEN FLT OF TWO MIL FGT AND AN ACR ACFT. OPERATIONAL ERROR.

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I WAS VECTORING; FGT X; FLT OF 2; FOR A VISUAL APCH TO BERGSTROM AFB FROM APPROX 20 NORTHWEST. I ASSIGNED A HEADING OF 150 DEG TO ALIGN THE FORMATION ON FINAL FOR A STRAIGHT IN. I ASKED FGT X IF HE HAD BERGSTROM IN SIGHT AND WAS INFORMED THAT HE DID. I CLRED X FOR A VISUAL APCH TO RWY 17R OVERHEAD PATTERN TO MAINTAIN 3000' UNTIL PAST AUSTIN ARPT. FGT X CONTINUED TO TURN TO AN APPROX HEADING OF 170 DEG WHICH ALIGNED HIM STRAIGHT IN TO AUSTIN ARPT. AS VISIBILITY WAS ONLY 7 MILES; I FELT IT POSSIBLE THAT X HAD MISTAKEN AUSTIN FOR BERGSTROM. I MADE SURE THAT AUSTIN TWR (WHO ALREADY HAD A POINT OUT) WAS AWARE OF FGT X POSITION.) I ADVISED X THAT HE WAS APPROX 1 MILE RIGHT OF COURSE AND TOLD HIM TO TURN LEFT TO HEADING 150 DEG TO LINE UP ON FINAL. I VERIFIED THAT X HAD BERGSTROM AFB IN SIGHT; AGAIN CLRED HIM FOR A STRAIGHT IN VISUAL AND TOLD HIM TO CONTACT BERGSTROM TWR. HE ACKNOWLEDGED AND I HEARD HIM TELL THE WING MEN TO GO TO TWR FREQ. THE FLT CONTINUED ACROSS THE FINAL ON THE SAME HEADING IN A SLOW DESCENT. AT THIS TIME ACR Y BROKE GND FROM AUSTIN RWY 13R. HEADING EAST; THE ACFT PASSED EACH OTHER APPROX 3 EAST OF AUSTIN WITH ACR Y CLIMBING FROM 2700' AND THE 2 FGT'S DESCENDING THROUGH 2400.