ACR FLC FAILS TO SHUT DOWN ENG AT GATE PRIOR TO LEAVING ACFT.

Narrative

AS WE APCHED THE GATE I STARTED UP THE APU; AND I CALLED THE SAFETY ZONE CLR. THE CAPT THEN SHUT DOWN THE L ENG AND WE TAXIED INTO THE GATE. I CALLED THE APU ON LINE AND THE CAPT SET THE BRAKES. I DID MY FLOW TO TURN THE PACK SWITCHES TO HIGH PRESSURE BLEED OFF; TURNED ON THE APU AIR; SINCE WARM AIR CONDITION WAS REQUIRED; AND OPENED THE PNEUMATIC XFEED VALVE. THEN I NOTICED THAT THE PACKS WERE OSCILLATING BACK AND FORTH AND DID NOT STABILIZE. I THEN TURNED THE L PACK OFF; WAITED A SECOND TO SEE IF IT WOULD STABILIZE AND IT DID. I BELIEVE I STARTED THE POST ENG SHUTDOWN FLOW AND I BELIEVE THE CAPT CALLED FOR THE PARKING CHK. AFTER A RUN THROUGH THE PARKING CHK; AS IT WAS THE LAST LEG OF THE TRIP (BUT NOT THE ACFT); THE CAPT ASKED FOR THE IN TIMES WHILE HE DID THE LOGBOOK AND I DID THE ACAR'S. THE CAPT GOT UP AND WENT IN THE BACK TO SAY GOOD-BYE TO THE FLT ATTENDANTS AND LEFT. I STAYED AND SAID GOOD-BYE TO MOST OF THE REMAINING PEOPLE UNTIL A WHEELCHAIR ARRIVED FOR A PAX -- I FELT IN THE WAY SO I SAID GOOD-BYE TO THE LEAD FLT ATTENDANT AND I LEFT. UPON ARRIVING HOME 5 HRS LATER THERE WAS A MESSAGE TO CALL THE CHIEF PLT. TO MY SURPRISE HE INFORMED ME THAT WE HAD LEFT THE REMAINING ENG RUNNING AT THE GATE. I COULD NOT BELIEVE THIS. LOOKING BACK ON THE DAY; WITH OVER 13 HRS OF DUTY (8.3 HRS BLOCK) AND 5 LEGS IN WINTER IFR; AND NO TIME TO EAT A NORMAL MEAL; I WAS TIRED AT THE COMPLETION OF THIS TRIP.