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Traditional models of motor control typically operate in the domain of continuous signals such as spike rates, forces, and kinematics. However, there is growing evidence that precise spike timings encode significant information that coordinates and causally influences motor control. Some existing neural network models incorporate spike timing precision but they neither predict motor spikes coordinated across multiple motor units nor capture sensory-driven modulation of agile locomotor control. In this paper, we propose a visual encoder and model of a sensorimotor system based on a recurrent neural network (RNN) that utilizes spike timing encoding during smooth pursuit target tracking. We use this to predict a nearly complete, spike-resolved motor program of a hawkmoth that requires coordinated millisecond precision across 10 major flight motor units. Each motor unit enervates one muscle and utilizes both rate and timing encoding. Our model includes a motion detection mechanism inspired by the hawkmoth's compound eye, a convolutional encoder that compresses the sensory input, and a simple RNN that is sufficient to sequentially predict wingstroke-to-wingstroke modulation in millisecond-precise spike timings. The two-layer output architecture of the RNN separately predicts the occurrence and timing of each spike in the motor program. The dataset includes spikes recorded from all motor units during a tethered flight where the hawkmoth attends to a moving robotic flower, with a total of roughly 7000 wingstrokes from 16 trials on 5 hawkmoth subjects. Intra-trial and same-subject inter-trial predictions on the test data show that nearly every spike can be predicted within 2 ms of its known spike timing precision values. Whereas, spike occurrence prediction accuracy is about 90%. Overall, our model can predict the precise spike timing of a nearly complete motor program for hawkmoth flight with a precision comparable to that seen in agile flying insects. Such an encoding framework that captures visually-modulated precise spike timing codes and coordination can reveal how organisms process visual cues for agile movements. It can also drive the next generation of neuromorphic controllers for navigation in complex environments.