The wide bandgap material, Gallium Nitride (GaN), has emerged as the dominant semiconductor material to implement high-electron mobility transistors (HEMTs) that form the basis of RF electronics. GaN is also an excellent material to realize photoconductive switches (PCSS) whose high-frequency performance could exceed that of RF HEMTs. In this paper, we numerically model the output characteristics of a GaN PCSS as a function of the input electrical and optical bias and the device dimensions. Importantly, we show that operating the GaN PCSS in the regime of negative differential mobility significantly benefits its high-frequency performance by compressing the temporal width of the output current pulse, while also enhancing its peak value. We find that when the optically excited carriers are generated in the middle of the active region, the bandwidth of the device is approximately 600 GHz, while delivering an output power exceeding 800 mW with a power gain greater than 35 dB. The output power increases to 1.5 W, and the power gain exceeds 40 dB with a near-terahertz bandwidth ( ≈ 800 GHz), as the laser source is moved closer to the anode. Finally, we elucidate that under high optical bias with significant electrostatic screening effects, the DC electric field across the device can be boosted to further enhance the performance of the GaN PCSS.