Static nonreciprocal forces between particles generically drive persistent motion reminiscent of self-propulsion. Here, we demonstrate that reciprocity-breaking fluctuations about a reciprocal mean coupling strength are sufficient to generate this behavior in a minimal two-particle model, with the velocity of the ensuing active bound state being modulated in time according to the nature of these fluctuations. To characterize the ensuing nonequilibrium dynamics, we derive exact results for the time-dependent center of mass mean-square displacement and average rate of entropy production for two simple examples of discrete- and continuous-state fluctuations in one dimension. We find that the resulting dimer can exhibit unbiased persistent motion akin to that of an active particle, leading to a significantly enhanced effective diffusivity.