The Mars Science Laboratory Curiosity rover has encountered both ancient lithified and modern active aeolian dune deposits within Gale crater, providing an opportunity to study how aeolian processes have changed during Gale crater's geological history. This study uses data from the Chemistry and Camera (ChemCam) and Chemistry and Mineralogy (CheMin) instrument suites onboard Curiosity to; (1) constrain the diagenetic processes that lithified and altered the ancient aeolian Stimson formation, (2) investigate whether the geochemical signature in the Stimson formation is consistent with the aeolian mafic-felsic mineral sorting trend identified in the modern Bagnold dune fields in Gale crater, and (3) discuss the provenance of the Stimson sediments, comparing it to those identified in the modern dune and ancient river and lake deposits also analyzed along Curiosity's traverse. The ancient Stimson dune deposits that stratigraphically overlie the Gale fluvio-lacustrine units were analyzed in two locations; the Emerson and the Naukluft plateaus. ChemCam data show that the Stimson formation has subtle variations in MgO, Al₂O₃, Na₂O, and K₂O between the two localities. An agglomerative cluster analysis of the constrained Stimson dataset reveals five clusters, four of which relate to different proportions of mafic and felsic minerals analyzed by ChemCam. In general, the cluster analysis shows that the Emerson plateau has a greater proportion of mafic minerals and fewer coarse, felsic grains relative to the Naukluft plateau. This variation in mafic and felsic minerals between localities suggests a southwest to northeast net sediment transport direction due to aeolian mineral sorting dynamics preferentially transporting mafic minerals that are easier to saltate than the elongate, often coarser, felsic minerals. This derived transport direction for the Stimson formation supports that determined by sedimentological evidence and is opposite to that previously determined for the active Bagnold dunes inferring a change in the wind regime with time. An opposite sediment transport direction between the ancient and modern dunes in Gale crater further supports geochemical and mineralogical evidence that suggests different basaltic source regions. Compositionally, the bulk Stimson formation is most similar to the subalkaline basalt source region that is inferred to be the dominant sediment source of the fluvio-lacustrine Bradbury group. This is likely the result of the Stimson formation and basaltic Bradbury group sediments sharing a similar local basaltic source region such as the rim and walls of Gale crater.