CL600 CREW REPORTS NOT BEING AWARE OF TAXIWAY CLOSURE WHEN TOWER IS NOT OPERATING.

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I WAS THE CAPT. WE HAD A REDUCED REST OVERNIGHT IN SAV WITH AN XA05 RPT TIME AND AN XA50 DEP. THE TWR IN SAV DID NOT OPEN UNTIL XB00. WE RECEIVED OUR CLRNC FROM ZJX AND ELECTED TO DEPART RWY 9. I BEGAN TAXIING OUT TXWY E AND CAME TO A RED ROW OF LIGHTS ACROSS THE TXWY. I WAS CONFUSED BECAUSE I KNEW THAT WAS NOT THE END OF THE RWY. I ASSUMED THAT IT WAS THE ILS HOLD SHORT LINE AND SINCE THE WX WAS VMC; I COULD CONTINUE TO TAXI TO THE END OF THE RWY. IT WAS JUST BEFORE SUNRISE AND VERY DARK SO I DIDN'T SEE THE SIGN BY THE ILS HOLD LINE AT E1 UNTIL I HAD TURNED BACK ONTO TXWY E THAT THE TXWY WAS CLOSED UNTIL THE TWR OPENED AT XB00. THE TWR CTLR MUST HAVE OBSERVED MY DILEMMA AND TURNED OFF THE ILS HOLD LINE AND TURNED ON THE TXWY LIGHTS W OF E1 SO WE COULD CONTINUE OUR TAXI. WE TOOK OFF AT XA59 JUST PRIOR TO THE TWR OPENING. IT WAS MY FIRST TIME DEPARTING SAV PRIOR TO THE TWR BEING OPEN AND MY FIRST EXPERIENCE WITH AN ILS HOLD LINE WITH A CLOSED TXWY DURING THE HRS WHERE THE TWR WAS NOT IN OP. ONCE I REALIZED I HAD MADE AN ERROR; I IMMEDIATELY STOPPED; AND CONTINUED ONLY AFTER THE TXWY LIGHTS HAD TURNED ON. I CONTRIBUTE MY ERROR TO FATIGUE AND LACK OF FAMILIARITY WITH THE NON-TWR OP. AFTER LATER REVIEW OF THE ARPT DIAGRAM; I SAW THE NOTE IN REGARD TO THE TXWY. I BELIEVE I OVERLOOKED THE NOTE DUE TO THE FINE PRINT AND POOR LIGHTING; FACTORING IN THE FATIGUE CAUSED BY THE BREVITY OF THE OVERNIGHT. ALTHOUGH THE REST WAS LEGAL; I DON'T THINK IT WAS SUFFICIENT CONSIDERING THE LENGTH OF DUTY DAYS PREVIOUSLY FOR SAFETY.