The recently introduced concept of Stokes fluctuations generalizes both the Hanbury Brown-Twiss effect and the notion of scintillation. Here we apply this new framework to the specific example of a Gaussian Schell-model (GSM) beam. We derive formulas for Stokes scintillations and Stokes fluctuation correlations, which explicitly express the dependence of these quantities on the GSM source parameters. It is found that the normalized Stokes scintillations vary significantly with position. Also, they can be either positively or negatively correlated.