B737-400 DIVERTS DUE TO RED NOSE GEAR UNSAFE LIGHT AFTER GEAR RETRACTION. LANDING NORMAL.

Narrative

AFTER TKOF UPON GEAR RETRACTION DURING AFTER TKOF CHKLIST; NOTICED RED NOSE GEAR LIGHT ILLUMINATED. I BELIEVED NOSE GEAR IN UP POS; NO NOISE OR VIBRATION. WE OBSERVED QRH PROCS AND SPD LIMITATIONS. THEN CONTACTED DISPATCHER VIA ACARS TO SEE IF MAINT COULD HELP DIAGNOSE AND IF COMPANY WANTED US TO CONTINUE. WE WERE TANKERING FUEL SO IT WOULD NOT HAVE BEEN A PROB. THE DISPATCHER VIA ACARS TOLD US MAINT WANTED US TO GO TO ZZZ. WE ADVISED FLT ATTENDANTS AND PAX WE WERE DIVERTING TO ZZZ FOR A PRECAUTIONARY LNDG WITH AN APPROX TIME OF 20 MINS FOR AN ETA. ALSO DURING VECTORS TO ZZZ WE RECEIVED A MESSAGE FROM DISPATCH VIA ACARS THEY WANTED US TO RETURN TO ZZZ1 SO CUSTOMER SVC COULD BETTER HANDLE PAX'S RERTES. EXERCISED CAPT AUTH AND CONTINUED TO ZZZ BECAUSE WE HAD ALREADY COMPLETED BRIEFINGS AND ABNORMAL PROCS. DURING ARR INTO ZZZ WITH GEAR EXTENDED AND 3 GREEN GEAR LIGHTS; ON APCH FOR RWY 10R BOTH THE GREEN AND RED NOSE GEAR LIGHTS EXTINGUISHED AND BOTH BULBS TESTED GOOD. BECAUSE ALREADY ON APCH FOR LNDG; WE DECIDED TO DO A FLY-BY BY THE TWR TO HAVE A VISUAL ON GEAR POS. TWR VERIFIED GEAR IN DOWN POS. DURING VECTORS FOR ANOTHER APCH WE RE-DID QRH MATRIX AND VERIFIED THROUGH VIEWING PORT; WITH SOME DIFFICULTY; NOSE GEAR WAS DOWN AND DID A NORMAL LNDG.