The coupling between a chromophore and its surroundings can, in the event of environmental perturbations, result in a stochastic modulation of the chromophore's transition frequency, which in turn can cause fluctuations in the population of the excited state. We demonstrate that by using these fluctuations in population inversion as the spectroscopic variable, one can extract information on whether the random modulation of the chromophore follows a diffusion process or a jump process. The population fluctuations also discriminate between Markov and non-Markov fluctuations of the atomic frequency. In addition, we show that this observable allows, in certain regimes, to unambiguously determine whether the population fluctuations are due to atomic frequency noise, or due to noise in the irradiating laser field. Finally, through a dressed state analysis, we demonstrate that the response of a randomly modulated atom is similar to that of an unmodulated atom driven by a noisy field that has amplitude fluctuations in only one quadrature.