Oscillatory devices have recently attracted significant interest as key components of computing systems based on biomimetic neuronal spiking. An understanding of the time scales underlying the spiking is essential for engineering fast, controllable, low-energy devices. However, we find that the intrinsic dynamics of these devices is difficult to properly characterize, as they can be heavily influenced by the external circuitry used to measure them. Here we demonstrate these challenges using a VO2 Mott oscillator with a sub-100-nm effective size, achieved using a nanogap cut in a metallic carbon nanotube electrode. Given the nanoscale thermal volume of this device, it would be expected to exhibit rapid oscillations. However, due to external parasitics present within commonly used current sources, we see orders-of-magnitude slower dynamics. We outline methods for determining when measurements are dominated by extrinsic factors and discuss the operating conditions under which intrinsic oscillation frequencies may be observed.