Proton exchange within the MH2 moiety of (TPB)Co(H-2) (CoH2; TPB = B(o-C(6)H(4)PiPr(2))(3)) by 2-fold rotation about the MH2 axis is probed through EPR/ENDOR studies and a neutron diffraction crystal structure. This complex is compared with previously studied (SiP3iPr)Fe(H-2) (FeH2) (SiP3iPr = [Si(o-(C6H4PPr2)-Pr-i)(3)]). The g-values for CoH2 and FeH2 show that both have the JahnTeller (JT)-active E-2 ground state (idealized C-3 symmetry) with doubly degenerate frontier orbitals, (e)(3) = [|m(L) +/- 2>](3) = [x(2) y(2), xy](3), but with stronger linear vibronic coupling for CoH2. The observation of H-1 ENDOR signals from the CoHD complex, 2H signals from the CoD2/HD complexes, but no H-1 signals from the CoH2 complex establishes that H-2 undergoes proton exchange at 2 K through rotation around the CoH2 axis, which introduces a quantum-statistical (Pauli-principle) requirement that the overall nuclear wave function be antisymmetric to exchange of identical protons (I = 1/2; Fermions), symmetric for identical deuterons (I = 1; Bosons). Analysis of the 1-D rotor problem indicates that CoH2 exhibits rotor-like behavior in solution because the underlying C3 molecular symmetry combined with H-2 exchange creates a dominant 6-fold barrier to H-2 rotation. FeH2 instead shows H-2 localization at 2 K because a dominant 2-fold barrier is introduced by strong Fe(3d)-> H-2(sigma*) pi-backbonding that becomes dependent on the H-2 orientation through quadratic JT distortion. ENDOR sensitively probes bonding along the L2ME axis (E = Si for FeH2; E = B for CoH2). Notably, the isotropic H-1/H-2 hyperfine coupling to the diatomic of CoH2 is nearly 4-fold smaller than for FeH2.