Neuromorphic computing implemented with spiking neural networks is an energy efficient computing paradigm to break through the Von Neumann bottleneck in the future. Ovonic threshold switching (OTS) selector is considered to be a promising spiking neuron candidate. As ≈1011 artificial neurons are needed for brain‐inspired computing, leakage current of OTS devices would waste enormous power. OTS devices with ultralow leakage current are deeply desired. Since the leakage current is closely related to the bandgap of OTS materials and only the amorphous one shows the volatile switching property, here binary gallium sulfide (GaS), characterized by 2.53 eV large band‐gap and ≈550 °C high crystallization temperature is singled out, as the most appealing OTS material. High‐density trap states, an essential prerequisite of the OTS material, are detected in the amorphous GaS. Indeed, the OTS behaviors of the GaS‐based device are directly observed. The simple OTS device could provide 21.23 MA cm−2 large ON current density, and ≈10−8 A low OFF current and ≤10 ns switching speed. Furthermore, it is also used to build GaS‐based leakage integrate and fire neurons for future neuromorphic computing. This study provides a new idea for material design before device preparation and takes a neuron as an example.