A GULFSTREAM 5 FLT CREW FAILS TO MEET XING RESTR DUE TO IMPROPER USE OF THE AUTOPLT.

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WE HAD BRIEFED APCH TO RWY 28R AND PROGRAMMED THE FMS FOR RWY AND APCH; ALONG WITH DSCNT ALTS. SUN WAS IN OUR EYES. WE HAD THE ARPT INITIALLY; BUT A FOG BANK BEGAN ROLLING IN ON THE RIDGES; OBSCURING THE APCH END AT 5 MI. BASES (CLOUDS) WERE ABOUT 3000 FT OTHERWISE CLR. PF WAS ON FMS; PNF SET UP FOR NAV #2 LOC AND GS. ON HEADING FOR APCH; CTLR THEN CLRED US TO INTERCEPT 095 DEG RADIAL SFO; FOR QUIET APCH AND CLRED TO DSND ON ARR. PF THOUGHT AUTO FEATURE OF FLT DIRECTOR WOULD AUTO CAPTURE 095 DEG RADIAL AND FLY INBOUND. HOWEVER; THIS; WE FOUND OUT ONLY HAPPENS ON LOC WITH 'APCH' SELECTED; NOT 'LOC.' SINCE FMS CONSIDERED IT TIME TO SWITCH FROM WAYPOINT AT 6000 FT TO WAYPOINT AT 4000 FT. THERE WAS NO MESSAGE AND DSCNT LOOKED NORMAL; UNTIL PNF XCHKED HIS NAV DISPLAY WHILE DOING CHKLIST. WE DSNDED THROUGH 6000 FT APPROX 3-4 MI EARLY; BUT VISUALLY HAD THE ARPT. CAUGHT AND ARRESTED DSCNT AT 4300 FT. ATC CANCELLED ARR CLRNC AS CROSSED ABEAM 4000 FT WAYPOINT REQUIREMENT. LESSON: USE THE AUTOMATION TO AID PLT; NOT WASTE PRECIOUS TIME TRYING TO MAKE AUTOMATION WORK; ESPECIALLY NEAR THE GND. CALI SIT ALL OVER AGAIN!