A C172 INSTRUCTOR WITH A STUDENT PRACTICING A LOC BACK COURSE RWY 25 APCH COMES IN CLOSE PROX TO A PA32 ON SHORT FINAL. THE C172 COMMENCED A CLBING L TURN TO AVOID THE OTHER ACFT. THE PA32 PLT FOLLOWED THE WRONG ACFT TO THE ARPT RATHER THAN FOLLOWING THE C172.

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MY STUDENT AND I WERE PRACTICING APCHS AT ORL EXECUTIVE LOC BACK COURSE RWY 25. ORLANDO APCH HANDED US OFF TO EXECUTIVE TWR. TWR SAID TFC TO FOLLOW 1/2 MI FROM RWY ON FINAL. WE WERE ROUGHLY 3 MI OUT. RPTED NO CONTACT ON TFC. WE WERE CLRED TOUCH AND GO. WE DSNDED TO OUR MDA (480 FT) AND WERE ON COURSE. APPROX 1 MI OUT WE WERE JUST ABOUT TO DSND FOR THE RWY WHEN AN AIRPLANE (NOT THE SAME ACFT ON A 1/2 MI FINAL) APPEARED IN THE UPPER R HAND CORNER OF THE WINDSHIELD AND DSNDED TO THE BOTTOM L CORNER OF THE WINDSHIELD; NOT AN EXAGGERATION. THE ACFT WAS 20 FT IN FRONT OF US TURNING BASE TO FINAL. WE MADE A CLBING L TURN AND CONTACTED TWR; STATING THE NEAR MIDAIR. TWR APOLOGIZED AND SO DID THE OTHER ACFT. APPARENTLY THE OTHER ACFT WAS SUPPOSED TO FOLLOW US. HE RPTED TFC IN SIGHT HAVING A HIGH WING AND WE NEVER SAW ACFT. ALSO BEING ON THE R SIDE; MY VISION WAS BLOCKED MORE BY THE WING AND MY STUDENT WAS UNDER THE HOOD. THE ACFT WAS A PIPER SARATOGA. ONE THING THAT REALLY BOTHERED ME WAS HOW RELAXED ATC AND THE OTHER ACFT TOOK THIS. FOR BEING THIS CLOSE -- THIS SHOULDN'T HAVE BEEN TAKEN SO LIGHTLY. SUPPLEMENTAL INFO FROM ACN 381548: TRAINING/CHK OUT PA32 TFC PATTERN. TWR CALLED #2 BEHIND CESSNA. BOTH LOOKED AND CALLED TFC 'WING UP.' SUN REFLECTION -- WAITED FEW SECONDS AND TURNED BASE. OTHER ACFT SAID NEAR MISS AND CUT HIM OFF. WE MUST HAVE SEEN SOMETHING OTHER THAN AN AIRPLANE 'WING UP.'