To unravel which processes are responsible for changes in atmospheric CO2 the carbon isotopes are useful helpers widely applied in the past. This study helps to better understand long-term changes in 13C, which has also consequences for the interpretation of atmospheric δ13CO2 measured together with CO2 in ice cores. The 13C cycle of the Plio-Pleistocene, as recorded in δ13C of benthic foraminifera, has power in periodicities related to the long eccentricity cycle of 405-kyr that is missing in corresponding climate records (e.g. δ18O). Using a global carbon cycle model I show that the long eccentricity cycle in δ13C might have been caused by variations in the isotopic signature of geological sources, namely of the weathered carbonate rock (δ13Crock) or of volcanically released CO2 (δ13Cv). This closure of the 13C cycle in these peridicities also explains the offset in atmospheric δ13CO2 seen between the penultimate and the last glacial maximum. The necessary isotopic signatures in δ13Crock or δ13Cv which align my simulations with reconstructions of the 13C cycle on orbital timscales have most power in the obliquity band (41-kyr) suggesting that land ice dynamics are the ultimate cause for these suggested variations. Since the Asian monsoon as reconstructed from speleothems has also an obliquity-related component it is possible that these proposed changes in weathering are indeed, at least partly, connected to the monsoon as previously suggested. Alternatively, the suggested impact of land ice or sea level on volcanic activity might also be influential for the 13C cycle. This indirect influence of ice sheets on the long eccentricity cycle in δ13C implies that these processes might not have been responsible for the 405-kyr periodicity found in ice-free times of the pre-Pliocene parts of the Cenozoic. See preprint (https://doi.org/10.5194/cp-2024-63) for details.