A B737-300 CREW DEPARTED WITHOUT CONSULTING A QRH OR MAINTENANCE AFTER AN AUTO BRAKE DISARM LIGHT WOULD NOT EXTINGUISH. THE FLIGHT HAD A WHEELS UP TIME THAT THE CAPTAIN DID NOT WANT TO LOSE. NO TAKEOFF IS ALLOWED WITH AN AUTO BRAKE DISARM LIGHT ON.

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PRIOR TO DEPARTING ZZZ THE 'AUTO BRAKE LIGHT' WOULD NOT EXTINGUISH. WE HAD A 'WHEELS UP TIME' AND I WAS TRYING TO MAKE SURE WE MADE THE DEP TIME. I ELECTED TO TURN OFF THE 'AUTO BRAKE SWITCH' AND CONTINUE THE TKOF. THE RWY (28R) WAS DRY AND WE HAD PLENTY OF STOPPING MARGIN. AFTER LEVELING OFF AT CRUISE ALT I STARTED TO INVESTIGATE THE LIGHT AND DISCOVERED THAT I SHOULD NOT HAVE TAKEN OFF AND SHOULD HAVE CONTACTED DISPATCH AND MEL'ED THE AUTO BRAKES. WE LANDED ZZZ1 WITH THE 'AUTO BRAKES' OFF; USING RWY 31C (DRY). UPON ARR I CONTACTED MAINT; LOGGED THE DISCREPANCY; AND BRIEFED THE ONCOMING CAPT. LESSONS LEARNED: 1) I SHOULD NOT HAVE TRIED TO HURRY SO WE WOULD NOT MISS THE 'WHEELS UP' TIME. 2) ANYTIME YOU MOVE A SWITCH AND THE SYS DOES NOT DO WHAT IT IS SUPPOSED TO; THEN SLOW DOWN AND INVESTIGATE. 3) I THOUGHT THAT I COULD JUST TURN OFF THE SWITCH AND GET IT LOOKED AT A MAINT BASE ZZZ1. 4) THIS WAS MY FO'S FIRST MONTH ON THE LINE AND THIS WAS A BAD EXAMPLE OF HOW NOT TO DO THE PROPER PROCS. SLOW DOWN AND DO NOT LET OUTSIDE LIMITS DICTATE YOUR ACTIONS. SUPPLEMENTAL INFO FROM ACN 813458: AT CRUISE ALT WE DECIDED TO FINALLY CONSULT THE QRH; AND WE DISCOVERED THAT WE SHOULD NOT HAVE DEPARTED WITHOUT CONTACTING DISPATCH AND MAINT AND PROPERLY FOLLOWED THE MEL PROCS. THE CAPT INFORMED MAINT OF THE DISCREPANCY UPON ARRIVING AND PROPERLY WROTE IT UP IN THE LOGBOOK. TAKE THE TIME TO INVESTIGATE ALL WARNING INDICATIONS; NO MATTER HOW INSIGNIFICANT OR SMALL YOU THINK THEY ARE. DO NOT LET TIME PRESSURES; SUCH AS PUSH TIMES OR ATC VOID TIMES; CAUSE YOU TO RUSH YOUR NORMAL PROCS. ALWAYS FOLLOW YOUR FLOW AND CHKLISTS AND RESPOND TO ANY AND ALL ABNORMALITIES.