Globular Clusters (GCs) are now well known to almost universally show multiple popu-lations (MPs). The HST UV Legacy Survey of a large number of Galactic GCs in UV filters optimized to explore MPs finds that a small fraction of GCs, termed Type II, also display more complex, anomalous behavior. Several well-studied Type II GCs show intrinsic Fe abundance variations, suggesting that the other, less well-studied, Type II GCs should also exhibit similar behavior. Our aim is to perform the first detailed metallicity analysis of NGC 1261, an intermediate mass Type II GC, in order to determine if this object shows an intrinsic Fe variation. We determined the Fe abundance in eight red giant members using Magellan-MIKE and UVES-FLAMES high-resolution, high S/N spectroscopy. The full range of [Fe/H] for the entire sample from the spectra is from -1.05 to -1.43 dexwith an observed spread sigma_obs=0.133 dex. Compared with the total internal error of Sigma_tot=0.06,this indicates a significant intrinsic metallicity spread of Sigma_int=0.119 dex. We found a very similar variation in [Fe/H] using an independent method to derive the atmospheric parameters based on near-IR photometry. More importantly, the mean metallicity of the five presumed normal metallicity stars is -1.37+/-0.02, while that of the three presumed anomalous/highmetallicity stars is -1.18+/-0.09. This difference is significant at the $pm$2.4Sigma level. We find indications from existing data of other Type II GCs that several of them presumedto have real metallicity spreads may in fact posses none. The minimum mass required for a GC to acquire an intrinsic Fe spread appears to be $pm$10^5 Msun. We find no strong correlation betwee nmass and metallicity variation for Type II GCs. The metallicity spread is also independent of the fraction of anomalous stars within the Type II GCs and of GC origin.