Following the use of the Mg-doped GaN for p-channel transistor channels, the manipulation of holes and their interactions with phonons, impurities, and dislocations remains a fundamental challenge. p-channel GaN electronics have received recent interest due to the relatively high hole mobility in AlN-GaN polarization induced two-dimensional hole gases (2DHGs). Although the mobility-limiting scattering mechanisms in 2DHGs is understood, the origins of 1/f noise in these channels is not. We introduce a characterization technique and stochastic model to identify 1/f noise mechanisms in a two-dimensional electron gas which can be extended to the 2DHG.