FLL FLT INSTRUCTOR ON TWIN REFRESHER FLT HAS NMAC IN NON TWR TFC PATTERN.

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I AM A FAA FLT INSTRUCTOR AT THE FAA ACADEMY IN OKLAHOMA CITY. I WAS TEACHING A LIGHT TWIN REFRESHER COURSE TO AN FAA INSPECTOR. THIS LESSON WAS ON VISUAL MANEUVERS AND WE WERE LNDG AT EL RENO; OK; FOR A BREAK AND WAS NOT PRACTICING TOUCH AND GO LNDGS. WE CALLED THE UNICOM FROM THE PRACTICE AREA FOR (AND RECEIVED) AN ARPT TA. WE CALLED AND ANNOUNCED OUR POS ON DOWNWIND LEG AND BASE TURNING FINAL JUST PRIOR TO TURNING FINAL TO RWY 17. WHILE WE WERE IN THE PRACTICE AREA THE UNICOM ADVISED US THERE WAS AN SMT IN THE PATTERN. ENRTE TO THE PATTERN I HEARD THE SMT MAKE A RADIO XMISSION THAT WAS WEAK IN VOLUME. I UNDERSTOOD HIM TO SAY OR THOUGHT HE SAID HE WAS ON DOWNWIND LEG. WHILE WE WERE ON THE DOWNWIND LEG I THOUGHT HE SAID HE WAS CLR OF RWY 17. AGAIN HIS VOLUME WAS WEAK. I CLRED THE AIRPLANE IN ALL DIRECTIONS VISUALLY EACH TIME WE TURNED OUR AIRPLANE; AND NEVER SAW THE SMT. THE SMT WAS YELLOWISH BROWN THE COLOR OF THE DEAD GRASS IN DECEMBER IN OKLAHOMA. AFTER LNDG THE PLT OF THE SMT CAME TO US AND SAID THAT WE HAD CUT HIM OUT OF THE PATTERN WHEN WE TURNED FINAL. HE MADE NO XMISSION AT THAT TIME WHEN HE SAID HE WAS GOING AROUND OR TURNING XWIND. IN THE FUTURE I WILL ASK PLTS WHO MAKE WEAK XMISSIONS TO SPEAK MORE LOUDLY AND CLARIFY THEIR POS IN THE TFC PATTERN TO ME IF I AM NOT SURE. ALSO I WILL KEEP A MORE VIGILANT VISUAL LOOK OUT.