Spike trains recorded from the cortex of behaving animals can be complex, highly variable from trial to trial, and therefore challenging to interpret. A fraction of cells exhibit obvious trial-averaged, task-related responses such as pure tone frequency tuning in auditory cortex. However, a substantial number of cells do not appear to fire in a task-related manner and are often neglected from analysis. Previous work used a novel single-trial, spike-timing-based analysis to show that both classically and non-classically responsive cortical neurons contain significant information about sensory stimuli and behavioral decisions suggesting that non-classically responsive cells may play an underappreciated role in perception and behavior. A recent study presented at Cosyne 2021 introduced a novel, task-performing spiking recurrent neural network (RNN) model incorporating excitatory and inhibitory spike-timing-dependent plasticity (STDP) that successfully recapitulates the distribution of classically and non-classically responsive neurons measured from the cortex of behaving animals. Here, we leverage this model to explore the synaptic origin and functional contribution of heterogeneous response profiles. Detailed inactivation experiments revealed that both response types contribute to task performance albeit via distinct mechanisms providing evidence for a double-dissociative function of these subpopulations. Excitatory and inhibitory plasticity rules independently increased the fraction of non-classically responsive units however both were required in tandem to improve performance and maintain engagement of all network units. We discovered unique local synaptic signatures that explain the heterogeneity of single-unit response profiles and made predictions that we compared to in vivo whole-cell recordings taken from the auditory cortex of behaving animals. Remarkably, parameters derived in silico accurately predicted the spiking response profiles of individual in vivo neurons. Our approach successfully accounts for the synaptic origins of heterogeneous neural responses and provides a powerful lens for exploring large-scale neuronal dynamics and the plasticity rules that shape them.