What was found
(CAN) ENGINE SHUTDOWN INCIDENT. MFG CONSULTED. ENGINE STARTED AND RAN FINE IMMEDIATELY AFTER LANDING. ACFT DISPATCHED FOR NON-REVENUE TRAINING AFTER INSP, COMPLETED 6 HOURS WITH NO ISSUES. FLOAT SWITCH STUCK IN "FULL" POSITION IN AUX TANK AND FUEL PRESSURE SWITCH FOR MOTIVE FLOW VALVE ALSO STUCK OPEN. ALLOWED MOTIVE FLOW VALVE TO REMAIN OPEN, KEPT THE SUPPLY OF MOTIVE FLOW FUEL TO AUX TANK JET PUMP RUNNING, AFTER AUX TANK WAS EMPTY. JET (VENTURI) PUMP CONTINUED TO SUPPLY FUEL UNTIL TANK WAS EMPTY, THEN PUMPED AIR THOUGH JET PUMP INTO NACELLE TANK. NACELLE TANK BECAME PRESSURIZED, WHICH PROHIBITED FUEL FROM GRAVITY FEEDING TANK. EVENTUALLY THE "LOW FUEL" ANNUNCIATOR CAME ON, WHEN ENGINE HAD BURNED ENOUGH FUEL OUT OF THE NACELLE TANK, ENGINE FLAMED OUT. THERE IS NO COCKPIT INDICATION TO CREW THAT AUX TANK IS TRANSFERRING, ONLY AN INDICATION THAT IT IS NOT TRANSFERRING, WHICH IS WHEN FLOAT SWITCH SHUTS OFF. EXPERIENCED NUMEROUS FAILURES OF FLOAT SWITCH IN PAST, THIS 1 HAD BEEN REPLACED WITH ONE REMOVED FROM ANOTHER ACFT APPROX 1 MONTH BEFORE TO TROUBLESHOOT A PROBLEM WITH A NO TRANSFER LIGHT. WHEN SWITCH WAS REMOVED, MX NOTED IT WOULD OCCASIONALLY STICK IN THE "FULL" POSITION.