What was found
AFTER TAKE OFF , THE RIGHT FIRE WARNING T-HANDLE ILLUMINATED INTERMITTENTLY AND THEN STEADY. THE CREW TROUBLESHOT, BUT COULD NOT GET THE LIGHT TO EXTINGUISH, ALL ENGINE INDICATIONS WERE NORMAL AND VISUALLY THERE WERE NO SIGNS OF FIRE. RETURNED TO DEPARTURE AND LANDED WITHOUT INCIDENT. MAINTENANCE PERFORMED A VISUAL INSPECTION OF THE RT ENGINE BAY FOR SIGNS OF ACTUAL FIRE, NO EVIDENCE FOUND. INSPECTED WIRING TO THE FLAME DETECTORS FOR CHAFING OR SIGNS OF DAMAGE WITH NO DEFECTS FOUND. PERFORMED A FUNCTIONAL CHECK OF THE FLAME DETECTOR CIRCUITS AND ALL THREE DETECTOR CIRCUITS TESTED SATISFACTORY. PERFORMED A GROUND RUN OF THE RIGHT ENGINE IN VARIOUS CONDITIONS WITH NO FIRE INDICATIONS, UNABLE TO DUPLICATE THE DISCREPANCY AND RETURNED THE AIRCRAFT TO SERVICE. DEPARTED AGAIN AND AT APPROX 8000FT MSL AND EXPERIENCED THE SAME ISSUE. RIGHT FIRE WARNING T-HANDLE FIRE DETECTOR ILLUMINATED AGAIN, ALL ENGINE INDICATIONS NORMAL AND VISUALLY, NO SIGNS OF FIRE. RETURNED TO DEPARTURE AND LANDED WITHOUT INCIDENT. MAINTENANCE VISUALLY INSPECTED THE RIGHT ENGINE AND NO EVIDENCE OF ACTUAL FIRE. TROUBLESHOT THE RIGHT FIRE WARNING T-HANDLE WIRING AND NO FAULTS WERE FOUND. PERFORMED FLAME DETECTOR FUNCTIONAL CHECK AND FOUND THAT THE NUMBER THREE TEST POSITION WAS NOT ILLUMINATING THE T-HANDLE. MAINTENANCE TESTED THE FLAME DETECTOR WITH AN INCANDESCENT LAMP TO CONFIRM THIS UNIT WAS DEFECTIVE, THE DETECTOR FAILED THE TEST. REMOVED AND REPLACED THE RIGHT FLAME DETECTOR AND OPS CHECKED NORMAL. THE AIRCRAFT WAS RETURNED TO SERVICE.