Isometric camera with a ground plane other than xz plane

Hello everyone,

I googled but couldn't find a similar problem. Here's my problem:

I'm making a game with isometric (30,45,0) degrees rotation of the orthographic camera. In certain points of the game. This way, the ground plane of my isometric setup is "xz plane" and up direction is "y direction" (where perpendicular lines to the ground plane has to be parallel to the left and right boundaries of viewing angle) . There is no problem with it. However in certain points of the game, i have to create an isometric camera with say "xy plane" is my ground plane and "-z" direction is my up direction.

In order to accomplish this isometric camera, I have calculated that my x,y,z rotations should be (-60,0,45). However it is definitely not isometric this way. Interestingly when i am looking at the (-60,0,0) setup and trying to change the z value by entering it in inspector panel, the camera is not rotating around global z axis, but it is rotating around its "looking direction axis" (and where the target it looks at does not change), as if i was rotating camera around z axis from (0,0,0) initial values(this way its looking direction axis is z axis).

I though if camera axis are z rotation always the look axis, y rotation always up axis, and x rotation always the remaining perpendicular axis(i.e the line connecting the hands when we hold the camera in real life). However when i start entering values on y axis from initial (-90,0,0) values(looking at global y direction and expecting to rotate around z axis), the target of the camera does not change again, it rotates around its look axis, which is the global y axis. More interestingly, starting at initial (-90,0,0), and entering values for either y or z rotation creates the same rotation, which is around global y axis, which i think is odd.

When i find the correct values for different isometric views on different planes, i will pass them to code.

My question is what am i missing here? and how can i create an isometric axis in different planes say xy plane being -z direction the up direction?