Fatty acid desaturase that catalyzes 2 consecutive steps in the biosynthesis of bombykol, a sex pheromone produced by the moth. First acts as an acyl-CoA Delta(11) desaturase (1) by catalyzing the formation of Delta(11) fatty acyl precursors. Then acts as a (11Z)-hexadec-11-enoyl-CoA conjugase (2) by converting a single cis double bond at position 11 of (11Z)-hexadec-11-enoyl-CoA into conjugated 10 trans and 12 cis double bonds. 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 (11Z)-hexadecenoyl-CoA + AH2 + O2 = (10E,12Z)-hexadecadienoyl-CoA + A + 2 H2O Highly expressed in the 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.