We investigate the dynamics of local operators in the simplest non-trivial modelof two qubits governed by the generator K(J, h) = JX1X2 + h(Z1 + Z2). Based onthe maximized commutator magnitude D12(s) = maxa,b∈{X,Y,Z} ∥[σs(a1), b2]∥op, whereσs(A) = eisKAe−isK, we construct a scalar characteristic of the operator dynamics. Aprecise three-branch formula is obtained: D(x, r) = max{F0(x), F1(x, r), Fmix(x, r)},where x = Js and r = h/J. The branches F0, F1, and Fmix possess explicit analyticalforms and correspond to the inter-qubit, field, and mixed contributions, respectively.We analytically describe the phenomenon of early blindness: at a fixed r > 0 andsufficiently short times, D(x, r) = F0(x) remains completely independent of the fieldparameter r. Furthermore, we identify blind lines at x = (2n + 1)π/4, where D = 2for all r > 0. These results provide a complete analytical description of the consideredobservable in the minimal two-qubit model.