Unexpectedly, we observe a strong Gaussian decay in the nuclear quadrupole resonance signal obtained from a powder sample of spin-1 nuclei under perturbation by off-resonant radio frequency pulses. Using a model composed of just pairs of nuclei, we theoretically determine that the decay is due to the homonuclear dipolar coupling being selectively unrefocused by the pulses. We find that the decay rate measures the dipolar coupling's strength, and permits us to determine how much of the sample's linewidth is due to homonuclear dipolar coupling versus electric field gradient inhomogeneity. Furthermore, knowing the strength, shape, frequency, and timing of the pulses that lead to this rapid decay is critical for the purposes of illicit substance detection, since it reduces signal and can lead to a false negative. We find that the experimental parameters that lead to this Gaussian decay are well explained by this simple model, which leads to a method for suppressing or revealing the decay. We confirm our theoretical understanding using two samples of sodium nitrite that vary in their broadening due to electric field gradient inhomogeneity by as much as a factor of three.