@erincandescent Okay, this makes sense when I think of a sphere with three vectors emanating from it representing the axes of rotation ("conveniently", these vectors are on the x,y,z axes of the 3D Cartesian space). Indeed, if I rotate my sphere about of these 3 axes 90 degrees, I can't tell the difference between the other 2.
However, when I replace my sphere with an actual gimbal, I have trouble visualizing it. Additionally, I never understood why quats/Euclid angles avoid the problem.