AFTER DIVERTING FOR A POSSIBLE FUEL SHORTAGE SIT AND DROPPING ITS BANNER TOO SOON; A LNDG; TAXIING; STINSON LOSES ITS R BRAKE AND A TXWY LIGHT DURING THE RESULTING TXWY EXCURSION AT ZZZ; US.

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I RPTED TO CPM ARPT FOR MY SECOND DAY OF BANNER TOW TRAINING. I SAT IN THE R SEAT AND WAS GIVEN THE DUTIES OF WATCHING FOR TFC AND LEARNING THE GENERAL OPS AND ROUTING OF THE BANNER FLTS. THE INSTRUCTOR AND I FLEW THE ROUTING FOR APPROX 2 HRS WHEN THE INSTRUCTOR NOTICED THAT THE AIRPLANE HAD MUCH LESS FUEL THAN HAD BEEN PLANNED FOR. AT THIS MOMENT; THE INSTRUCTOR DECIDED TO FLY TO THE NEAREST ARPT; ZZZ; WHERE HE PROCEEDED TO INFORM THE TWR OF THE LOW FUEL SIT. HE DID NOT DECLARE AN EMER; HOWEVER; HE INFORMED THEM OF THE CRITICAL AMOUNT OF FUEL ON BOARD THE AIRPLANE. HE SAID THAT THERE WAS APPROX BTWN 5 AND 15 MINS OF FUEL REMAINING. WE WERE CLRED TO LAND AND GIVEN PERMISSION TO DROP THE BANNER ON SHORT FINAL; ON THE GRASS LOCATED JUST N OF THE LNDG RWY. THE INSTRUCTOR RELEASED THE BANNER TOO EARLY AND A PORTION OF IT LANDED ON THE FREEWAY OFF RAMP JUST N OF THE GRASS FIELD; WHICH WAS INTENDED FOR BANNER DROP. THE BANNER WAS PICKED UP BY ARPT PERSONNEL; WITHOUT HAZARD TO ANY PERSONS OR PROPERTY. THE LNDG WAS MADE SUCCESSFULLY ON RWY AND WE WERE INSTRUCTED TO TURN L OFF THE RWY AND CONTACT GND CTL. THE AIRPLANE WAS SLOWED DOWN STRAIGHT AHEAD ON THE RWY AND THE INSTRUCTOR MADE THE AVAILABLE L TURN. UPON BRINGING THE AIRPLANE TO A STOP ON THE TXWY; THE INSTRUCTOR INFORMED ME THAT HIS R BRAKE HAD FAILED; AND HE ASKED ME FOR ASSISTANCE. THERE ARE NO BRAKES LOCATED IN MY SEAT; THE R SEAT; OF THIS AIRPLANE (STINSON 108). MY ATTEMPT TO HELP IN STOPPING THE CONTINUING L TURN WAS FUTILE. THE INSTRUCTOR THEN PULLED THE MIXTURE CTL; BRINGING THE PROP AND THE ENG TO A STOP; WHEN AN ACFT TIRE RAN OVER AND BROKE A TXWY LIGHT. THE AIRPLANE WAS ROLLING AT APPROX 5 MPH AT THIS TIME AND CAME TO A STOP SHORTLY AFTER. THERE WAS NO DAMAGE TO THE AIRPLANE; NOR ANY HARM DONE TO THE INSTRUCTOR OR I. THE INSTRUCTOR PERFORMED THE PREFLT. HOWEVER; AS A PLT WITH THE GENERAL KNOWLEDGE OF SMALL PISTON PWRED AIRPLANES; I DID ASSURE THAT THE AIRPLANE WAS FULL OF FUEL AND HAD ADEQUATE OIL BY VISUALLY INSPECTING EACH OF THOSE ITEMS PRIOR TO GETTING IN THE AIRPLANE. I WAS NOT PIC DURING THIS FLT; AND DID NOT PERFORM THE PREFLT ACTION. I DID OBSERVE THE INSTRUCTOR PIC CHK BOTH BRAKES DURING TAXI TO THE RUN-UP AREA; AND AGAIN AFTER RUN-UP. THERE APPEARED TO BE PRESSURE AND ADEQUATE BRAKING. WHERE THIS INCIDENT COULD AND SHOULD HAVE BEEN RESOLVED WAS DURING A PREFLT BRIEFING IN WHICH A DISCUSSION OCCURRED BTWN THE OWNER/OPERATOR AND THE INSTRUCTOR (PIC); ON THE SPECIFIC PERFORMANCE AND FUEL BURN OF THIS ACFT AS IT RELATED TO BANNER TOWING. SUPPLEMENTAL INFO FROM 619544: THE ACFT WAS FILLED WITH 40 GALS OF FUEL. RIGHT AFTER TKOF; I LOOKED AT MY WATCH AND NOTICED THERE WAS ABOUT 35 MINS DISCREPANCY; BTWN THE ACFT CLOCK AND THE WATCH. THE ACFT CLOCK WAS SLOW. I ADJUSTED IT; BUT DID NOT CHANGE THE TIME IN MY NOTES. I WAS PLANNING CONSERVATIVELY FOR 13 GPH. LATER; RECORDS WOULD SHOW A BURN OF 11.4 GPH. MY GOAL WAS TO BE BACK WITH 30 MINS OF FUEL ON BOARD. I ESTIMATED 3 HRS AND 4 MINS OF FUEL AT 13 GPH. I DETERMINED TO BE BACK 2 1/2 HRS AFTER ENG START. I MADE ANOTHER FUEL BURN ESTIMATE; BUT INCORRECTLY USED THE TIME THAT I HAD PUT IN MY NOTES BEFORE I NOTICED THE TIME DISCREPANCY. SOMETHING DIDN'T SEEM RIGHT; BUT I DECIDED TO DIVERT TO ZZZ IMMEDIATELY AND SORT OUT THE PROB ON THE GND. I ESTIMATE THAT I RELEASED ABOUT 3 SECONDS TOO EARLY BECAUSE PART OF THE BANNER LANDED ON AN ACCESS RAMP TO THE FREEWAY. BEFORE TURNING ONTO THE TXWY AND THE R BRAKE WENT ALL THE WAY TO THE FLOOR. THE ACFT TURNED L AND I PULLED THE MIXTURE TO STOP THE ENG. THE ACFT ROLLED ABOUT 10-15 FT MORE; STRUCK A TXWY LIGHT AND STOPPED. I HAD NEVER DROPPED A BANNER AT ZZZ; BEFORE AND I THINK NOW THAT; THE FACTORS WERE: UNFAMILIAR DROP ZONE; A VERY LARGE BANNER WHICH ACTED SOMEWHAT LIKE A SAIL; AND THIS WAS MY 1ST FLT SINCE VACATION WITH ABOUT 6 WKS INBTWN FLTS. NORMALLY; I HAVE A GND CREW TO ADVISE WHEN THE BANNER IS IN IDEAL POS. ALSO; NOT CHANGING THE TIME IN MY NOTES DEFINITELY CAUSED CONFUSION ANDAN UNNECESSARY DIVERSION.