I've continued to work on my Gaussianity tests for S5 L1 data. 

Following the statistical measure in Ando et al. (2003), I've calculated the Laguerre coefficient, c2, for all frequencies present in my S5 L1 PSD as a metric of Gaussianity. When c2 is zero, the distribution is Gaussian. A positive c2 corresponds to glitchy noise, while a negative c2 suggests stationary noise.

Below is a plot displaying variation in c2 for this PSD:

By observing the c2 value and histogram of distribution of various PSD values at a given frequency, we can elucidate statistical differences in the Gaussian nature of noise at that frequency which are unclear in the standard PSD.