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Memristors based on 2D semiconductors such as MoS2 and its derivative materials exhibit analog switching behaviors capable of emulating some synaptic functions, including short-term plasticity, long-term potentiation, and spike-time-dependent-plasticity. Additional investigation is needed to realize reliable control of such synaptic behaviors for practical device implementation. To meet this scientific need, we fabricated MoS2-based memristors and studied their paired-pulse facilitation (PPF) and long-term memory characteristics under different pulse programming settings. This research has provided a guideline for identifying the programming settings for different neuromorphic processes. For example, a specific setting resulting in PPF > 30% and long-term conductance change < 20% has been identified to be suited for processing real-time temporal information. Furthermore, this research also indicates that the MoS2 memristor keeps having an almost constant relative change in conductance but greatly enhanced drive current level under laser illumination. This behavior can enable an easy integration of such memristive devices with state-of-the-art controller circuits for practice neuromorphic control applications.