RPTR BACK TAXIS WITHOUT CHKING WITH TWR ON CLOSED PORTION OF RWY.

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AFTER RECEIVING AN IFR CLRNC; GND CTL INSTRUCTED ME TO TAXI TO RWY 20 WITH AN INTXN DEP FROM TXWY 'A' DUE TO THE FIRST 120 FT OF THE RWY BEING CLOSED. AFTER RECEIVING TKOF CLRNC FROM LCL CTL I BEGAN TO BACK TAXI ABOUT 100 FT FOR A LITTLE ADDITIONAL TKOF DISTANCE. LCL CTL THEN ISSUED ME AN INSTRUCTION TO MAKE A 180 DEG TURN AND TKOF IMMEDIATELY AS I WAS NOT AUTH TO BACK TAXI ON THE CLOSED RWY PORTION. THERE WAS ALSO TFC TURNING A 2 MI FINAL WHICH COULD HAVE BEEN A CONFLICT. I IMMEDIATELY REVERSED DIRECTION; TOOK OFF AND EXITED THE AREA WITHOUT FURTHER INCIDENT OR PROB. THIS PROB AROSE DUE TO MY NOT BEING AWARE THAT AN INTXN DEP FROM TXWY 'A' WAS ON THE CLOSED PORTION OF THE RWY. RWY CLOSURE MARKINGS WERE INADEQUATE. THERE WAS BUT 1 THIN LINE PAINTED ON THE RWY DOWNFIELD FROM TXWY 'A' THAT WAS NOT VISIBLE FROM THE COCKPIT. HAD I KNOWN I WAS ALREADY ON THE CLOSED PORTION OF THE RWY I WOULD NEVER HAD BACK TAXIED AT ALL. REGARDLESS OF THE FACT HOWEVER; I KNOW BETTER THAN TO MAKE UNAUTH 180'S OR BACK TAXI'S ON RWYS. THAT WAS AN ERROR ON MY PART NEVER TO BE REPEATED. THIS INCIDENT COULD HAVE BEEN PREVENTED HAD THERE BEEN BETTER SIGNAGE; MARKINGS; AND BARRIER PRESENT TO INDICATE THE CLOSED RWY SIT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: THE RPTR STATED HE WAS FLYING A PRESSURIZED CESSNA 414. IT WAS A HOT DAY AND HE WANTED TO HAVE ALL THE RWY POSSIBLE FOR HIS LIGHT TWIN. THE THOUGHT DID NOT OCCUR TO HIM THAT THE RWY WAS CLOSED BUT IN HIND SIGHT HE REALIZED HE SHOULD HAVE TOLD THE TWR WHAT HE WAS PLANNING TO DO BEFORE THE R TURN TO BACK TAXI RATHER THAN WHAT THE TWR WOULD NORMALLY EXPECT; A L TURN FOR TKOF. THE RWY WAS ACTUALLY CLOSED AT THE POINT WHERE THE RPTR TURNED ON TO THE RWY FROM TXWY 'A' BUT THAT WAS WHAT THE TWR WANTED. THE RWY IS NO LONGER CLOSED IN THAT AREA SO THE ISSUE IS ACADEMIC AS FAR AS SIGNS AND MARKINGS ARE CONCERNED. THERE HAS BEEN NO ACTION FROM THE FAA AGAINST THE RPTR FOR HIS BACK TAXI.