S-adenosyl-L-methionine-dependent protein methyltransferase that trimethylates the N-terminal glycine 'Gly-2' of elongation factor 1-alpha (TEF1 and TEF2), before also catalyzing the mono- and dimethylation of 'Lys-3' (PubMed:21858014, PubMed:26545399). May be involved in rDNA silencing and in lifespan determination (PubMed:12736687). Present with 7280 molecules/cell in log phase SD medium. Belongs to the class I-like SAM-binding methyltransferase superfamily. EFM7 family. Was originally thought to be a nicotinamide N-methyltransferase.