Nonlinear transport of a semi-insulating (SI) GaAs photodetector in a semiconductor gas discharge structure (SGDS) is studied experimentally for a wide range of gas pressures p, interelectrode distances d and different diameters D of the detector areas. While being driven with a stationary voltage, the system generates current and discharge light emission (DLE) instabilities with different amplitudes of the oscillations. The transformation of the profile and amplitude of the current density of the filaments in the different regions of the current-voltage characteristic (CVC) has been studied. Instabilities of spatially non-uniform distributions resulting in the formation of multiple current filaments with increasing voltages above the critical values have been observed. It is shown that the interelectrode distance only plays a passive role and is not responsible for the appearance of the DLE instability under the experimental conditions. At the same time, the expanded range of current and DLE oscillations are observed for different diameters D of the infrared (IR) photodetector areas. An SGDS with an N-shaped CVC is analysed using both the current and DLE data which show the electrical instability in the GaAs photodetector. It is found that the application of high feeding voltage to this photodetector gives rise to a non-uniform spatial distribution of the DLE, which disturbs the operation of the system. The experiment also presents a new method to study and visualize the electrical instabilities in a high-resistivity IR photodetector of large diameter.