NMAC FOR 2 LIGHT ACFT IN THE CIRCUIT AT EYW.

Narrative

DURING A VFR FLT TO KEY WEST; A SKYMASTER (X) CAME CLOSE TO A PIPER NAVAJO (Y) DURING THE FINAL PORTION OF THE APCH SEQUENCE. THE WX WAS CLR HOWEVER; DUE TO THE SUN SETTING ON THE HORIZON AND THE DIRECTION OF FLT; THE VISIBILITY TOWARDS THE W WAS NIL. THE SKYMASTER (X) WAS APCHING FROM THE NE WITH THE INTENTION OF LNDG. THE TWR WAS EXTREMELY BUSY WITH ARRIVING/DEPARTING ACFT BANNER TOWING ACFT AND SEA PLANES DOING LOW LEVEL JOINS TO LAND. THE SKYMASTER (X) WAS FINALLY GIVEN A CLRNC TO JOIN MID-FIELD DOWNWIND FOR A L-HAND CIRCUIT. HOWEVER; THE SKYMASTER (X) WAS WELL N OF THE ARPT AND WAS PAST THE THRESHOLD OF THE RWY IN USE (RWY 9) WHEN THE CLRNC WAS RECEIVED (4.9 KN I NW OF THE ARPT -- GPS READING). AN S-TURN COULD HAVE BEEN FLOWN TO REPOSITION THE ACFT DOWNWIND BUT DUE TO THE CURRENT CONGESTION AND THE ADVISORY MADE BY ATC THAT THEY WERE EXTREMELY BUSY; THE SKYMASTER MAINTAINED A WESTERLY DIRECTION TO STAY CLR OF THE TFC PATTERN IN USE (L-HAND). EVENTUALLY THE ATC REQUESTED THE POS OF THE SKYMASTER (X) WHICH WAS NOW WELL W OF THE AIRFIELD TURNING S (5.2 KN MI FROM THE THRESHOLD -- GPS READING) TO ENTER THE TFC PATTERN AND JOIN OVERHEAD FOR A L-HAND DOWNWIND AS PREVIOUSLY CLRED. THE SKYMASTER (X) XMITTED HIS INTENTIONS TO THE ATC AS THEY STARTED THE RETURN TO THE TFC PATTERN. DURING THIS TIME; THE ATC CLRED ANOTHER INCOMING ACFT (PIPER NAVAJO 'Y') TO JOIN IN A R-HAND DOWNWIND FOR LNDG. THE NEAR MISS OCCURRED (SAME PLANE -- 300 FT AWAY) THEREAFTER. IN THE L-HAND TURN TOWARDS THE OVERHEAD BOTH CREW MEMBERS WERE LOOKING FOR THE OTHER ACFT THAT ATC HAD GIVEN INSTRUCTION TO JOIN FOR RWY 9. BECAUSE OF PREVIOUS SEAPLANE TFC FLYING AT 500 FT AND BELOW IT WAS ASSUMED THAT PROPER SEPARATION WAS MAINTAINED ALTHOUGH; THEY WERE SURPRISED THAT BOTH SIDES OF THE ACTIVE; IE; L SIDE AND R SIDE (WHAT WAS THOUGHT TO BE THE DEAD SIDE; UNTIL INSTRUCTIONS TO THE PIPER NAVAJO (Y) WAS HEARD FROM THE TWR BY THE SKYMASTER (X)). THE PIPER NAVAJO (Y) CONTINUED TO FLY A R BASE TO LAND.