B757 FLC EXECUTES MISSED APCH AT LIM AND ENCOUNTERS STICK SHAKER ON GAR.

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WE WERE ON THE SALINAS 2 ARR INTO LIMA; AND WE WERE CLRED TO DSND DOWN TO 2000 FT AND CLRED FOR THE ILS RWY 15. THE CAPT WAS PF; AND WE WERE HIGH ON THE PROFILE XING SIGAS. WE WERE STILL HIGH AT THE FAF WITH PWR AT IDLE AND THE SPD BRAKES DEPLOYED. 2000 FT WAS STILL IN THE ALT WINDOW; AND THE AUTOPLT ATTEMPTED TO CAPTURE THE ALT; BUT THE CAPT HELD THE THROTTLES TO IDLE. THE AUTOPLT TRIMMED THE ACFT TO FULL AFT (NOSE UP) IN AN ATTEMPT TO MAINTAIN ALT AND THEN DISCONNECTED. THE CAPT INITIALLY CONTINUED THE DSCNT HAND FLYING AND THEN DECIDED TO GO AROUND. WHEN HE PUSHED TOGA; THE ACFT PITCHED UP DRAMATICALLY AND WE GOT THE PITCH LIMIT INDICATOR AND STICK SHAKER. THE CAPT PUSHED THE NOSE OVER ABRUPTLY; WHICH RESULTED IN SEVERAL SIGNIFICANT PITCH OSCILLATIONS (BECAUSE THE PITCH TRIM WAS SO FAR AFT). THE RELIEF PLT POINTED OUT THE TRIM PROB; WHICH NONE OF US HAD NOTICED PRIOR TO THAT POINT. THE ACFT WAS RETRIMMED AND CLEANED UP AND NORMAL FLT WAS RE-ESTABLISHED ON THE GAR. WE WERE VECTORED FOR ANOTHER APCH; WHICH CONCLUDED WITHOUT FURTHER INCIDENT. I WAS NOT AS PROACTIVE AS I NEEDED TO BE PRIOR TO THE ACTUAL INCIDENT. I SHOULD HAVE SUGGESTED HOLDING AT SIGAS TO DSND AND GET BACK ON PROFILE; AND I SHOULD HAVE SUGGESTED A GAR SOONER. IN ADDITION; I WAS NOT AS AWARE OF WHAT THE AUTOMATION AND AIRSPD WERE DOING; AS I NEEDED TO BE. SUPPLEMENTAL INFO FROM ACN 569324: DURING THE ILS RWY 15 APCH INTO LIM; WE WERE CLRED VIA A STRAIGHT -- IN ILS APCH. WE TURNED INBOUND TO INTERCEPT THE LOC; BECAUSE WE WERE HIGH ON THE APCH DSNDING OUT OF FL60-2000 FT DIRECT TO KILAR; THE CAPT ELECTED TO DSND FULLY CONFIGURED (FLAPS 25 DEGS) AND SPD BRAKES DEPLOYED. WE NEVER INTERCEPTED GLIDE PATH; THE ACFT CAPTURED 2000 FT MCP ALT. AT THAT POINT; IDLE PWR WAS SELECTED AND A VERT SPD DSCNT WAS SELECTED. SHAKER AND GAR/RECOVERY HAPPENED ALMOST IMMEDIATELY. A PIO AND SHAKER WAS ENCOUNTERED DURING THE RECOVERY DUE TO THE TRIM COMMANDS OF THE AUTOPLT (11 UNITS). SUBSEQUENT ILS RWY 15 APCH WAS UNEVENTFUL. AS RELIEF PLT; I FEEL THAT I SHOULD HAVE BEEN MORE FORCEFUL IN CHALLENGING THE WISDOM OF DSNDING CONFIGURED; BOARDS DEPLOYED IN ORDER TO CAPTURE A STRAIGHT IN GS. THE OBVIOUS REMEDY WAS TO SHOOT THE FULL WHISKEY DSCNT PROFILE AND ESTABLISHING A STABILIZED DSCNT FOR THE ILS APCH. I ALSO SHOULD HAVE BEEN BETTER ATTUNED TO THE DANGER OF A/S CTL ONCE WE LEVELED OFF AND DID NOT CHANGE THE CONFIGURATION.