What was found
WE WERE CLIMBING SOMEWHERE IN THE LOW 20’S. WE THEN NOTICED THE MASTER CAUTION FLASHING. A QUICK SEARCH OF THE PANEL ALSO REVEALED THE LEFT ENGINE FIRE LIGHT TO BE FLASHING. WE THEN PULLED THE LEFT POWER LEVER TO IDLE FOR 15 SECONDS AS PER THE MEMORY ITEMS. THE LIGHT FAILED TO EXTINGUISH IN THE 15 SECONDS SO WE THEN PULLED THE LEFT T HANDLE AND WAITED A SECOND, WITH THE FIRE LIGHT STILL FLASHING WE FIRED ONE OF THE FIRE BOTTLES INTO THE LEFT ENGINE. AFTER A FEW SECONDS AND THE FIRE LIGHT STILL FLASHING, WE FIRED THE SECOND FIRE BOTTLE INTO THE LEFT ENGINE. I THEN CALLED OFF AND WE COMPLETED THE ENGINE FIRE-SHUTDOWN CHECKLIST. ATC WAS INFORMED EARLY IN THIS PROCESS AND WE WERE IN THE PROCESS OF DESCENDING AND DIVERTING TO KBHM. WE SHOT THE APPROACH AND LANDED IN KBHM WITHOUT INCIDENT. A POST FLIGHT INSPECTION BY THE FIRE DEPARTMENT AND THEN US PILOTS DID NOT REVEAL ANY SIGNS OF AN ACTUAL ENGINE FIRE, LEADING US TO BELIEVE THAT IT WAS AN ISSUE WITH A SENSOR.