For the first time, the consequences of combining two well-established empirical relations that describe different aspects of the spectral evolution of observed gamma-ray burst (GRB) pulses are explored. These empirical relations are (1) the hardness-intensity correlation and (2) the hardness-photon fluence correlation. From these we find a self-consistent, quantitative, and compact description for the temporal evolution of pulse decay phases within a GRB light curve. In particular, we show that in the case in which the two empirical relations are both valid, the instantaneous photon flux (intensity) must behave as 1/(1 + t/τ), where τ is a time constant that can be expressed in terms of the parameters of the two empirical relations. The time evolution is fully defined by two initial constants and two parameters. We study a complete sample of 83 bright GRB pulses observed by the Compton Gamma-Ray Observatory and identify a major subgroup of GRB pulses (~45%) which satisfy the spectral-temporal behavior described above. In particular, the decay phase follows a reciprocal law in time. It is unclear what physics causes such a decay phase.