Quantum transit times have a long history of inequivalent definitions, including phase times, dwell times, and quantum-clock constructions. In this context we revisit the Salecker–Wigner–Peres stationary quantum clock as a phase-sensitive scattering observable, with clock time defined by the energy derivative of the transmission phase shift across the interaction region. For real compactly supported one-dimensional potentials, we show that the raw stationary Peres clock generically contains a universal (1/) continuum-edge term whose coefficient is fixed by low-energy scattering data. For the attractive square well, this threshold singularity is inherited from the vanishing exterior momentum and the associated scattering matching, rather than from resonant delay itself. We derive the exact stationary clock time for the square well and introduce a threshold-subtracted clock observable that removes the leading singularity for each fixed nonexceptional potential. Comparison with the dwell time and the transmission Wigner phase delay identifies a local Lorentzian contribution near sufficiently isolated resonances. The approach to a zero-energy resonance is nonuniform, however, and limits the use of this subtraction to isolate a resonance at the continuum edge. A symmetric barrier–well–barrier cavity and a numerical asymmetric two-step attractive well provide complementary controls.