Abstract Recent work has revealed two classes of globular clusters (GCs), dubbed Type I and Type II. Type II GCs are characterized by both a blue and a red red giant branch composed of stars with different metallicities, often coupled with distinct abundances in the slow neutron-capture elements (s-elements). Here we continue the chemical tagging of Type II GCs by adding the two least massive clusters of this class, NGC 1261 and NGC 6934. Based on both spectroscopy and photometry, we find red stars in NGC 1261 to be slightly enhanced in [Fe/H] by ∼0.1 dex and confirm that red stars of NGC 6934 are enhanced in iron by ∼0.2 dex. Neither NGC 1261 nor NGC 6934 show internal variations in the s-elements, which suggests a GC mass threshold for the occurrence of s-process enrichment. We found a significant correlation between the additional Fe locked in the red stars of Type II GCs and the present-day mass of the cluster. Nevertheless, most Type II GCs retained a small fraction of Fe produced by SNe II, lower than the 2%; NGC 6273, M54, and ω Centauri are remarkable exceptions. In the Appendix, we infer for the first time chemical abundances of lanthanum, assumed as representative of the s-elements, in M54, the GC located in the nucleus of the Sagittarius dwarf galaxy. Red-sequence stars are marginally enhanced in [La/Fe] by 0.10 ± 0.06 dex, in contrast with the large [La/Fe] spread of most Type II GCs. We suggest that different processes are responsible for the enrichment in iron and s-elements in Type II GCs.