What was found
AFTER TAKEOFF AND UPON PLACING THE GEAR TO THE UP POSITION THE HYD PRESS ON ANNUNCIATION REMAINED ON AND THE RED GEAR UNSAFE LIGHT ANNUNCIATION AND THE PUMP CONTINUED TO STAY RUNNING. FIRST OFFICER CALLED FOR THE HYD PRESS ON EMERGENCY PROCEDURES CHECKLIST. THE HYD PRESS ON WAS IDENTIFIED, CONFIRMED, AND CHECKLIST COMPLETED. THE CREW CYCLED THE LANDING GEAR TO THE DOWN POSITION. DURING TRANSIT THE CREWS IDENTIFIED AIRFLOW DISTURBANCES FOLLOWED BY THREE GREEN (NOSE, LH, RH) WITH THE RED GEAR UNSAFE LIGHT EXTINGUISHED AND DECIDED TO LEAVE THE GEAR IN THE DOWN POSITION AND FLAPS AT APPROACH. THE CAPTAIN ELECTED TO BE CAUTIOUS AND INFORMED ATC THAT THEY WOULD RETURN TO KAPA AND PERFORMED ONE LOW APPROACH OVER THE RUNWAY FOR TOWER TO GIVE A VISUAL LOOK, AND THE CONTROLLER REPORTED N414FW YOUR LANDING GEAR APPEARS TO BE DOWN. THE CAPTAIN DECLARED AN EMERGENCY FOR WHAT APPEARED TO BE AN ABNORMAL CHECKLIST ITEM AND LANDED WITHOUT INCIDENT.