A B737-500 #1 ENG HAD A TAILPIPE FIRE AFTER LNDG WHEN THE FO; MEANING TO SECURE THE #2 ENG; ACCIDENTALLY MOVED THE #1 ENG FUEL CTRL LEVER OFF THEN BACK ON.

Narrative

UPON LNDG AT ZZZ ON RWY XX AND EXITING ON TXWY XX; INTO THE RAMP AREA VIA Y LINE TOWARD GATE X. THE FO WAS MULTI-TASKING DOING THE AFTER LNDG FLOW; SPEAKING WITH RAMP CTL AND THEN COMPANY RADIO. I ASKED THE FO TO SHUT DOWN ENG #2. AT WHICH POINT HE WAS CLRING THE R SIDE FOR THE PENDING TURN INTO THE GATE; HE GRABBED THE #1 FUEL LEVER BY MISTAKE. AS HE TURNED HIS HEAD INSIDE TO VERIFY THE LEVER; HE ALSO STARTED TO LOWER THE FUEL LEVER. UPON IMMEDIATELY REALIZING THAT HE HAD STARTED TO LOWER THE WRONG LEVER; HE RAISED THE LEVER BACK UP. A FEW SECONDS LATER RAMP CTL ADVISED US OF A FIRE/FLAMES COMING OUT OF OUR #1 ENG. ALTHOUGH THERE WERE NO INDICATIONS OF ANY ENG FIRE IN THE COCKPIT; THE FO PERFORMED THE QRC MEMORY ITEMS FOR TAILPIPE-FIRE AND SHUT DOWN THE #1 ENG. RAMP THEN CONFIRMED NOT SEEING ANY FURTHER FLAMES OUT OF THE #1 ENG. AS A PRECAUTION I REQUESTED THAT CRASH/FIRE RESCUE MEET US AT THE GATE. AS A SIDE NOTE AND AS ANY GOOD PLT WILL DO; WE HAVE REVIEWED THE EVENTS MANY TIMES. TO THIS END WE CAN ONLY ADD SOME POSSIBLE CONTRIBUTING FACTORS: 1) A LONG DAY FOR THE FO; THAT STARTED BY A COMMUTE AT 11 AM. WHICH LED TO 2 CANCELED FLTS AND FINALLY GETTING ON HIS LAST FLT; MAKING FOR A LONG FATIGUING BY XA40 WHEN THE EVENT OCCURRED. 2) A LONG DAY FOR THE CAPT THAT STARTED WITH A WAKE UP CALL BY THE CREW DESK BY 6 AM; TO BE NOTIFIED FOR 'A 6 PM TRIP.' 3) GETTING TO ZZZ1 AND THEN HAVING TO WAIT FOR OUR LATE ARRIVING INBOUND ACFT. WAITED 1 HR. 4) MENTAL STRESS DUE TO THE FO POSSIBLY BEING FURLOUGH AGAIN. 5) DISTR OF MULTI-TASKING 2 RADIO CALLS; AFTER LNDG FLOW; LOW LIGHT CONDITIONS IN THE COCKPIT AND CLRING TFC.