Paleoclimatic proxies for interannual variability reveal power within the 7--15 year quasi-decadal (QD) band in Earth's history. Despite the fact that the best-established sources of QD variability in modern climate are internal, this QD variability in paleoclimatic records is commonly attributed to the ~11 year sunspot cycle of solar variability. Intrinsic QD variability has received little attention in paleoclimatology. We apply two different modeling frameworks to assess the degree to which QD variability might have occurred in the past and question whether existing paleoclimate records, no matter how well-resolved, distinguish between internally driven and solar-driven variability. We show that even a simple atmospheric general circulation model (GCM), driven by constant solar radiation, produces climate oscillations with a period of ~11 years. Then, motivated by numerous studies arguing for the presence of sunspot cycles in Eocene (~50 Ma) paleoclimate records, we demonstrate that a fully coupled GCM simulation with constant solar forcing reproduces the full spectrum of reconstructed Eocene variability. In the examples we consider, there is no compelling reason to invoke solar cycles as a cause of interpreted variability. We stress the importance of identifying internal modes of variability from paleoclimate records to increase understanding of the climate system.