CE550 CPR ACFT ON VECTORS FOR APCH; ACFT #1 HSI MALFUNCTIONED RESULTING IN RPTR PLT BECOMING DISORIENTED. SUBSEQUENT TRACK DEV RESULTED IN A TCASII ON ACFT FOLLOWING RPTR.

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ON DEC/XX/97 AT XA50 MST; I WAS THE ACTING CAPT ON A CESSNA CITATION SII; DEPARTING FROM ROCK SPRINGS; WY; TO SLC. THE WX IN SLC WAS ABOVE MINIMUMS IN SNOW FOR ILS APCHS THE ENTIRE MORNING AND SLOWLY IMPROVING. I WAS INITIALLY CLRED TO CARTR INTXN TO HOLD AS PUBLISHED WITH APPROX A 30 MIN EFC TIME -- WHICH WAS EXTENDED DUE TO SNOW REMOVAL PROBS AT SLC. OUR FUEL QUANTITY WAS NEVER A PROB AND WE COULD HAVE HELD FOR MORE THAN AN HR LONGER THAN WE DID WITH RESERVES. I BELIEVE WE HELD FOR CLOSE TO AN HR IN ALL. DURING HOLDING WHILE IN A COUPLE OF THE COURSE REVERSALS THE PLT'S HSI #1 HDG FLAG APPEARED MOMENTARILY -- PERHAPS FOR A SECOND; AND THEN RETURNED TO NORMAL. THIS IS A CONTRIBUTING FACTOR. FROM HOLDING AT CARTR TO BEING VECTORED TO DOWNWIND FOR RWY 34L THE HDG FLAG NEVER APPEARED. UPON TURNING L FOR A VECTORED HDG OF 360 DEGS FROM 160 DEGS TO INTERCEPT THE LOC THE HDG FLAG AGAIN APPEARED BUT THE HSI #1 COMPASS SEEMED TO BE SLEWING NORMALLY WITH RMI #1 AND HSI #2. WITH THE HDG FLAG THE AUTOPLT COMMAND BARS WERE LOST AND THE YAW DAMPENER DROPPED OFF-LINE. I HAD BEEN FLYING BY HAND DURING THE ENTIRE VECTOR SEQUENCE. AS THIS MALFUNCTION WAS OCCURRING MY TASK SATURATION WAS HIGH -- FLYING THE ACFT AND ASCERTAINING WHAT FOR SURE HAD FAILED. IN THE SECONDS FROM THE POINT WHEN THE FLAG APPEARED TO WHEN I ROLLED OUT NEAR THE ASSIGNED HDG I NOTICED A SPLIT OF 40- 50 DEGS FROM RMI #1 AND HSI #2. THE APCH CTLR CAUGHT THIS SIMULTANEOUSLY AND MADE HIS R TURN INSTRUCTION. IN ACTUALITY I HAD TURNED THE PLANE TO A HDG OF 310-320 DEGS. THIS IS WHERE THE TCASII WAS ALERTED ON AN ACFT THAT WAS FOLLOWING US IN TRAIL. THERE WERE SEVERAL SECONDS OF CONFUSION OF EXACTLY WHAT HDG THE ACFT I WAS FLYING WAS ON UNTIL A XCHK WITH THE MAGNETIC COMPASS CONFIRMED THE HSI #2 TO BE ACCURATE. I IMMEDIATELY BEGAN A TURN BACK TO THE R USING RMI #1 AS MY HDG REF; INTERCEPTED THE LOC AND COMPLETED THE APCH USING RAW DATA. BEING THAT THE PLT'S HSI AND RMI #1 SEEMED TO SLEW IDENTICALLY DURING THE FIRST SECONDS OF THE TURN AFTER THE FLAG APPEARED I WAS DECEIVED ASSUMING THAT A GLITCH HAD AGAIN OCCURRED AS EARLIER IN HOLDING. ONCE THAT FLAG HAD SHOWN IF I HAD ASSUMED A HARD FAILURE AND USED THE RMI #1 AS A REF NO INCIDENT WOULD HAVE HAPPENED. I'VE ALREADY DISCUSSED THIS WITH THE SLC FSDO AND NO ENFORCEMENT WILL BE TAKEN BUT I FELT ASRS MIGHT APPRECIATE HEARING OF THIS INCIDENT. THEY SEEMED SYMPATHETIC THAT THIS FAILURE HAPPENED AT THE WORST POSSIBLE TIME DURING THE APCH. LESSON LEARNED.