FO OF A WDB FAILED TO FOLLOW THE LOC COURSE AFTER VECTOR FOR INTERCEPTION DUE TO THE AUTOPLT TURNING THE ACFT IN THE OPPOSITE DIRECTION WHICH RESULTED IN ATC INTERVENTION AND INSTRUCTIONS TO GAR. THE FO OVERSHOT MISSED APCH ALT AFTER ENGAGING THE GAR MODE AND HAD TO DSND BACK TO THE PRESCRIBED ALT.

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AT THIS TIME OF THE FLT; WE WERE ON AN INTERCEPT HDG FOR THE ILS TO RWY 13L AT JFK. THE AUTOPLT WAS ENGAGED IN 'HDG SELECT.' IMMEDIATELY AFTER APCH CLRNC 'LOC' WAS ENGAGED ON THE AUTOPLT. THE ANNUNCIATION ON THE ADI SHOWED LOC CAPTURE; HOWEVER; THE RAW DATA LOC WAS STILL INDICATING FULL SCALE DEFLECTION. SHORTLY AFTER; THE ACFT ROLLED L TO 35 DEGS OF BANK IN WHAT APPEARED TO BE AN ATTEMPT TO TRACK THE ILS OUTBOUND. AT THIS POINT WE WERE ON THE ILS AND GOING THROUGH ON AN EASTERLY HDG. I TURNED THE AUTOPLT OFF AND BEGAN A R TURN IN AN EFFORT TO TRACK THE ILS INBOUND. AT THIS POINT ATC ASKED WHAT WAS HAPPENING. WE RESPONDED AND HE SAID 'GAR.' OUR HDG WAS NOW 165 DEGS; MISSED APCH ALT WAS 3000 FT. WE WERE AT 2700 FT. I HIT THE GAR BUTTON WHICH GIVES GAR THRUST AND GIVES YOU A 2000 FPM RATE OF CLB. DUE TO THE WORKLOAD; TURB; HVY RAIN; COUPLED WITH CLEANING UP THE ACFT; WE CLBED TO 3400 FT. AGAIN ATC ASKED ABOUT OUR ALT AND WE RETURNED TO 3000 FT. I THINK THIS INCIDENT COULD HAVE BEEN AVOIDED IF IN TRAINING THEY GO OVER SOME SHORT ALT CLBS IN A GAR MODE. AUTOPLT FUNCTION TEST SHOULD BE CONDUCTED WKLY AS OPPOSED TO MONTHLY.