Catalyzes the formation of Delta(11) fatty acyl precursors in the pheromone gland, with a preference for myristic acid. an 11,12-saturated fatty acyl-CoA + 2 Fe(II)-[cytochrome b5] + 2 H(+) + O2 = an (11Z)-Delta(11)-fatty acyl-CoA + 2 Fe(III)-[cytochrome b5] + 2 H2O Detected in pheromone gland. The histidine box domains may contain the active site and/or be involved in metal ion binding. Belongs to the fatty acid desaturase type 1 family.