Business jet Captain reported receiving a low altitude terrain alert from ATC on approach to SUN. Landing was uneventful.

Narrative

Crew had discussed arrival into Sun Valley. Crew referenced Company charts as well as FOQA DATA. CREW BUILT THE VISUAL RUNWAY 31. Crew inserted a four nautical mile ring from CAKIR intersection. Pilot flying discussed the 340 heading after passing the four nautical mile distance to intercept the centerline of runway 31 once visual contact had been confirmed; pilot flying elected to deviate from course and fly closer to the hill to the east of centerline; I mentioned to the pilot flying that we were not on course; and that we should stay on course. Pilot flying asked if we were too close to the hill; to which I responded that we are not on the course which we had briefed to be on. Pilot flying stated he wanted to lineup with the center of the runway. I mentioned to the pilot flying that if we stayed on the company designated procedure; we would have plenty of time to line up with the center of the runway. At that time; we received warning to which the pilot flying turned away from the mountain. We never were in any danger of being too close to the mountain. Landing was uneventful. I believe the Crew did a great job of identifying the procedures flying into Sun Valley. We had discussed their arrival as well as headings and altitudes. The pilot flying elected to deviate. After bringing it to his attention; he indicated he wanted to get lined up with a runway; causing the terrain advisory. I did mention to him several times what the procedure was however; he did not want to listen. I never felt in danger; thus; I did not take the airplane away from him; and it was better to ensure positive control of the airplane.