A WARNING LIGHT INDICATING THE TAILCONE ASSEMBLY WAS ON; INDICATING THE TAILCONE AREA WAS NOT SECURE. GND MECH CLAIMED THERE WAS A FAULT IN THE INDICATING SYS. FLC FLIES ACFT AND THEN LEARNS AT DEST THAT TAILCONE WAS NOT SAFE FOR FLT.

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DURING PREFLT; FLC DISCOVERED 'TAILCONE UNSAFE' MESSAGE ILLUMINATED ON OVERHEAD ANNUNCIATOR PANEL. LCL MAINT WAS INFORMED. LEAD MECH INFORMED CAPT THAT THE TAILCONE SECTION OF THE ACFT WAS SECURE; AND A FAULTY WARNING SYS WAS RESPONSIBLE FOR WARNING MESSAGE. MECH RELATED HIS INTENT TO DEFER THE DISCREPANCY AS A MAINT CARRYOVER ITEM; ACCEPTABLE FOR FLT. I OBJECTED TO THIS; STATING THAT I THOUGHT IT WAS OF A MORE SERIOUS NATURE; AND REFUSED TO SIGN FOR THE AIRPLANE UNLESS THE DISCREPANCIES WERE REPAIRED. 15 MINS AFTER THIS DISCUSSION; THE MECH RETURNED; ANNOUNCING THAT THE PROB WAS FIXED BY ADJUSTING THE WARNING SWITCH IN THE TAILCONE SECTION. AIRWORTHINESS RELEASE WAS SIGNED BY THE MECH WITH NO LIMITATIONS; AND THE WARNING LIGHT WAS NO LONGER ILLUMINATED. DURING TKOF ROLL; APCHING V1; THE LIGHT REILLUMINATED; AND THE DECISION WAS MADE TO CONTINUE THE TKOF. ABNORMAL PROC WAS FOLLOWED; AND FLT CONTINUED TO JFK. ON INITIAL CONTACT WITH NEW YORK APCH CTL; I INFORMED THEM OF THE NEED TO PERFORM A RWY INSPECTION AFTER OUR LNDG; LOOKING FOR A POSSIBLE JETTISON OF THE TAILCONE DURING THE LATTER STAGES OF LNDG ROLLOUT. INSPECTION OF THE RWY AND AFT TAIL SECTION OF THE ACFT AFTER LNDG BY FIRE DEPT REVEALED NOTHING UNUSUAL. AFTER ARRIVING AT THE GATE AND THROUGH DISCUSSION WITH LCL MECH; I LEARNED THAT THE TAILCONE WAS INDEED IN AN UNSAFE CONDITION WITH LOOSE CTL CABLES IN UNRESTRAINED CONDITION; WHICH COULD HAVE LED TO JETTISON OF TAILCONE. ACFT REMOVED FROM SVC FOR REPAIR. ACTIONS OF MAINT AT DEP STATION RESULTED IN FLC FLYING AN UNAIRWORTHY ACFT. AFTER BEING ASSURED THAT IT WAS IN AN AIRWORTHY CONDITION.