Hi,
I've read a lot about 2D images which have a 3D-look in this forum. I would like to put in, what I learned from a very skilled (old school) photographer years ago (I hope he was right, but you can test that yourself):
An image look 3D, if you look at the image under the same angle you saw the scene in real life. If you move back from the image, the angle becomes smaller and the image appears flatter. If you move closer to the image the 3D look becomes more pronounced.
To test this you need a image - not too small - with a content that looks familiar to you, best shot with 80 mm on MF or 50 mm on 35mm. Then hang it on the wall and approach it. If you are far away the image will look flat. At some point it starts to look 3D, if you come to close it has a very pronounced 3D-look.
The reason lies in human perception and the way your brain thinks how things should be. A lot of 3D perception has to do with that. For example: In real live you have 3D vision by triangulation (two eyes and the point you are looking at) in a range up to 10 meters. Every 3D impression further away comes from experience, objects where you know their sizes. And your perception can be easily fooled. Stage designers do this a lot. See the movie "Play Time" by Jacques Tati, there is a whole city built this way.
Hope that is true and you can verify this with the little experiment I described above.
Best,
Johannes
P.S.: That also describes why telephoto images look flat and wide angles look very 3D under usual circumstances - they narrow or widen the angle. But, you can make a large print and choose the right distance and even tele shots look 3D or wide angle shots look flat.