The pilot and passenger departed on a flight to add fuel to the airplane’s fuel tanks. The airplane was originally manufactured with 2 main fuel tanks and 2 auxiliary fuel tanks. A modification installed 2 additional wingtip tanks that fed into the main tanks via transfer pumps. When in cruise flight, the pilot selected the main fuel tanks and turned on the wingtip tank transfer pumps. However, one light indicating that the pump was operating did not illuminate. The pilot reselected the auxiliary tanks and decided to return to his home airport. The pilot entered the airport traffic pattern and he selected the main fuel tanks but noted that “not much fuel [was] showing in the left main tank.” Due to traffic already in the pattern, the pilot had to perform additional maneuvering to remain clear and then reestablish a final approach. On short final, the pilot determined that the landing was assured and selected full flaps. Shortly after, the left engine stopped producing power. The pilot knew the airplane would not make the runway with the landing gear and flaps down. He performed an off-field landing resulting in substantial damage to the fuselage, elevators, and wings. The pilot informed a Federal Aviation Administration inspector that the reason for the loss of engine power was due to fuel mismanagement.