The 1,461-hour instrument rated private pilot reported that while departing on an instrument flight, the landing gear selector handle was raised to the retracted position and he observed that the green lights (down indication) went out, but the amber lights (up indication) did not illuminate. The pilot added that he attempted to use the manual gear pump to no avail. The pilot continued on with his proposed flight plan and advised air traffic control of his situation. The pilot recycled the gear selector handle several times and was not able to get a gear up or gear down indication. The pilot stated on the pilot/operator report (NTSB form 6120.1) "I elected to continue my planned flight to burn off as much fuel as reasonable, get as close to my destination as possible, and to reach good VFR conditions." The pilot made two low passes to have the tower personnel attempt to determine if the landing gear appeared down. The tower noted that the left main and the nose gear appeared to be down but that the right main gear appeared to be partially retracted and rotated. The pilot elected to land on an the 5,939-foot long, by 150-foot wide asphalt runway, which was oriented on a heading of 030 degrees. The airplane remained upright and slid-off of the runway to the right side when the airplane slowed. The pilot egressed without assistance and was not injured. A Federal Aviation Administrator inspector, who responded to the accident site, reported that the right main landing gear had collapsed and there was structural damage to the right horizontal stabilizer and the rudder. His investigation revealed that a frayed wire on the landing gear squat-switch terminal prevented power to the relay switch that controlled the landing gear activation. The weather at the airport at the time of the accident was reported as winds from 080 degrees at 8 knots, temperature of 34 degrees Celsius, with an altimeter setting of 30.03 inches of Mercury.