We propose a classification scheme for rotational bands built on nuclear scissors vibrations, based on a systematic analysis of the competition among distinct collective modes. Our analysis within the proton-neutron interacting boson model reveals that scissors-mode bands exhibit robust odd-even staggering in excitation energies, leading to multiple energy-splitting patterns in scissors rotations. Remarkably, despite their distinct origins, these splitting patterns share a common spectroscopic fingerprint: pronounced clustering between the two lowest band members with spin-parity 1+ and 2+. This behavior naturally accounts for the puzzlingly small separation between the two levels observed in 156Gd and establishes a general mechanism applicable to axially asymmetric nuclei and, potentially, to other two-fluid systems exhibiting scissors-mode collectivity. We also present theoretical predictions for the systematic evolution of this splitting across the deformed Gd isotopic chain, further corroborating the proposed mechanism.