What was found
AFTER TAKEOFF THE LANDING GEAR HANDLE WAS MOVED TO THE UP POSITION. BOTH MAIN GEAR RETRACTED BUT THE NOSE GEAR DID NOT RETRACT. THE ONLY INDICATION IN THE COCKPIT WAS ONE GREEN NOSE GEAR DOWN LIGHT. HOLDING WAS COORDINATED WITH ATC. EMERGENCY AND NORMAL CHECKLISTS WERE ACCOMPLISHED. NORMAL GEAR DOWN INDICATIONS WERE OBSERVED IN THE COCKPIT. A TOWER FLY-BY WAS ACCOMPLISHED TO CONFIRM THAT ALL LANDING GEAR APPEARED TO BE EXTENDED. AN EMERGENCY WAS NOT DECLARED AND TRAFFIC PRIORITY WAS NOT REQUESTED. AIRCRAFT WAS STOPPED STRAIGHT AHEAD ON RUNWAY AFTER LANDING AND MAINTENANCE PINNED GEAR BEFORE RESUMING TAXI TO RAMP. TROUBLESHOOTING FOUND LEFT NOSE GEAR DOOR PROX SWITCH INOP (CLOSED). ALSO FOUND NOSE GEAR UPLOCK PROX SWITCH INOP (CLOSED). REMOVED AND REPLACED BOTH PROX SWITCHES.