MLG FLC NOTIFIED DURING CLB BY FLT ATTENDANT THE SEAT BELT SIGN WAS NOT ON FOR TKOF.

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CLBING THROUGH APPROX 14000 FT; THE 'A' FLT ATTENDANT CALLED AND ASKED IF WE KNEW THE SEATBELT SIGN WAS NOT ON. YES; INDEED; IT WAS NOT ON -- HOW COULD THAT BE? WE HAD RUN THE CHKLIST. 'SEATBELT SWITCH -- ON' IS A RESPONSE ON THE BEFORE START CHKLIST AND WE HAD RUN THE LIST; SO HOW WAS IT MISSED? I USUALLY PHYSICALLY TOUCH THE SWITCH WHEN CHALLENGED. APPARENTLY THIS TIME I DIDN'T AND EITHER DID NOT CHK IT OR LOOKED OVER THE TOP OF MY BIFOCAL SUNGLASSES AND THOUGHT IT WAS IN THE 'ON' POS. EITHER WAY; IT WAS NOT ON. I ASKED THE 'A' FLT ATTENDANT WHEN SHE NOTICED IT AND HER RESPONSE WAS; 'ON TAXI OUT.' I ASKED WHY DIDN'T YOU SAY SOMETHING? SHE SAID; 'I DIDN'T WANT TO BOTHER YOU.' I TRY TO GIVE A VERY COMPLETE CREW BRIEFING PRIOR TO THE TRIP AND EMPHASIZE THE IMPORTANCE OF WORKING AS A TEAM. THIS WILL HAVE TO BE RE-EMPHASIZED IN LATER BRIEFINGS. I WILL ADMIT THE ENTIRE CREW WAS TIRED AT THIS POINT. THIS WAS DAY 2 OF 3. DAY 1 WAS 12 HRS PLUS AND 8 HRS FLYING TIME; MINIMUM CREW REST; 9 HRS + 45 MINS. DAY 2 WAS 11 HRS PLUS AND I THINK THE ENTIRE CREW JUST WANTED TO GET TO THE HOTEL AND GET SOME SLEEP. I KNOW I SLEPT 10 1/2 HRS THAT NIGHT. THE MORAL: FATIGUE; NOT PAYING ENOUGH ATTN TO A CHKLIST ITEM (OR NOT SEEING WHAT I THOUGHT I SAW); AND A BREAKDOWN IN CRM CAUSED AN ERROR -- A SMALL ONE; BUT NEVERTHELESS AN ERROR. ATTN AND GOOD CRM TECHNIQUES SHOULD BE THE ORDER OF THE DAY -- EVERY DAY.