Electrical impedance tomography (EIT) based tactile sensor offers significant benefits on practical deployment because of its sparse electrode allocation, including durability, large-area scalability, and low fabrication cost, but the degradation of a tactile spatial resolution has remained challenging. This article describes a deep neural network based EIT reconstruction framework, the EIT neural network (EIT-NN), alleviating this tradeoff between tactile sensing performance and hardware simplicity. EIT-NN learns a computationally efficient, nonlinear reconstruction attribute, achieving high-resolution tactile sensation and well-generalized reconstruction capability to address arbitrary complex touch modalities. We train EIT-NN by presenting a sim-to-real dataset synthesis strategy for computationally efficient generalizability. Furthermore, we propose a spatial sensitivity aware mean-squared error loss function, which uses an intrinsic spatial sensitivity of the sensor to guarantee a well-posed EIT operation. We validate an outperformance of EIT-NN against conventional EIT sensing methods by conducting a simulation study, a single-touch indentation test, and a two-point discrimination test. The results show improved spatial resolution, sensitivity, and localization accuracy. The beneficial features of the generalized sensing of EIT-NN were demonstrated by examining touch modality discrimination performance.