What was found
PER PILOT: FIRE WARNING AUDIBLE "CHIME" WITHOUT LIGHT WHILE IN FLIGHT ON RETURN LEG WITHOUT PATIENT WHILE DESCENDING FOR LANDING AT HOME BASE. NO SECONDARIES OBSERVED IN FLIGHT OR ON GROUND DURING SHUT DOWN. ON GROUND, POST NORMAL SHUTDOWN, NOTHING VISUALLY NOTICED ON POST FLIGHT INSPECTION. TROUBLESHOT FIRE WARNING TEST SWITCHES VIA BATTERY POWER; #1 WORKED NORMAL WITH BOTH LIGHT AND TONE. #2 WORKED NORMAL WITH BOTH LIGHT AND TONE INITIALLY BUT ON SUBSEQUENT TESTS THE LIGHT ALWAYS WORKED BUT THE CHIME TONE SOMETIMES DID NOT WORK AND OTHER TIMES THE AUDIBLE CHIME TONE DID WORK BUT WOULD NOT STOP AS IT SHOULD WHEN THE TEST SWITCH WAS TURNED BACK OFF. FLIGHT WATCH WAS NOTIFIED, MAINTENANCE REP WAS NOTIFIED, BASE LEAD WAS NOTIFIED. PER 135.415 SERVICE DIFFICULTY REPORT THIS INCIDENT MIGHT WARRANT REPORTING. UPON FURTHER TROUBLESHOOTING; CORESPONDING "FIRE" LIGHT ON THE #2 NOW ILLUMINATES WHEN AIRCRAFT IS POWERED ON BATTERY AND GPU. POWER WIRE TO #2, INBOARD FIRE DETECTOR IS FAULTING TO GROUND. TIGHTENED #2 FIRE DETECTOR CONNECTOR, SYSTEM OPERATIONAL CHECK GOOD.