Underwing versus on the back is not the same as why one on the vertical stabilizer or just the air intake there

If you have an odd number of engines you need to place one in the center line of the airplane and with a jet engine, you can put it in the front line with propellers.

You can but even the number of engines under the wing or on the body. 4 engines on the back have them placed side by side like a Vickers VC10

3 engines existed primarily because of ETOPS rating, you could fly longer over open water with 3 compared to 2 engines and the cost will be less than if you have 4 engines. A minor part is that it adds high-altitude takeoff performance in locations like Colorado which is at 1-mile altitude.

They have disappeared because engine performance and ETOPS regulations have changed so you are allowed to do the same flight with just 2 engines and it is a cheaper way to build and operate aircraft

Boeing 727 have all 3 engine in the rear, and McDonnell Douglas MD-11 had 2 under the wings and 1 in the back. So 2 engines under the wings or on the back are unrelated to the vertical stabilizer position of a third engine.