Ancient (>10 Gyr) globular clusters (GCs) show chemical abundance variations in the form of patterns among certain elements, e.g. N correlates with Na and anticorrelates with O. Recently, N abundance spreads have also been observed in massive star clusters that are significantly younger than old GCs, down to an age of similar to 2Gyr. However, so far N has been the only element found to vary in such young objects. We report here the presence of Na abundance variations in the intermediate age massive star clusters NGC 416 (similar to 6.5Gyr old) and Lindsay 1 (similar to 7.5Gyr old) in the Small Magellanic Cloud, by combining Hubble Space Telescope (HST) and European Southern Observatory Very Large Telescope MUSE observations. Using HST photometry, we were able to construct 'chromosome maps' and separate subpopulations with different N content, in the red giant branch of each cluster. MUSE spectra of individual stars belonging to each population were combined, resulting in high signal-to-noise spectra representative of each population, which were compared to search for mean differences in Na. We find a mean abundance variation of Delta[Na/Fe] = 0.18 +/- 0.04 dex for NGC 416 and Delta[Na/Fe] = 0.24 +/- 0.05 dex for Lindsay 1. In both clusters, we find that the population that is enhanced in N is also enhanced in Na, which is the same pattern to the one observed in ancient GCs. Furthermore, we detect a bimodal distribution of core-helium-burning red clump (RC) giants in the UV colour-magnitude diagram of NGC 416. A comparison of the stacked MUSE spectra of the two RCs shows the same mean Na abundance difference between the two populations. The results reported in this work are a crucial hint that star clusters of a large age range share the same origin: they are the same types of objects, but only separated in age.