The flight departed using fuel from the main fuel tanks to supply the engine and climbed to altitude. The pilot then utilized the fuel from the electrically driven auxiliary fuel system but stated that the engine quit 1 hour 15 minutes later. He determined that there was a failure or malfunction of the electrical system and fuel from the main tanks was then used to supply the engine. The engine was restarted. The flight diverted to an alternate and the pilot attempted to supply fuel to the engine from the auxiliary fuel tank by turning on the shutoff valve and both fuel pumps but was unsuccessful. The engine eventually quit due to fuel exhaustion in the main fuel tanks. He ditched the aircraft near an island, swam to it, and was rescued 26 hours later. The aircraft was not recovered. He further stated that he believes that the fuel pumps overloaded the electrical system but in retrospect believes the alternator failed. The auxiliary fuel system incorporates two electric pumps but only one is to be used for normal operation. The second pump is to be used only for a failure or malfunction of the first pump.