Catalyzes the formation of a Delta12 double bond, acting on monounsaturated fatty acyl substrates like palmitoleoyl-CoA ((9Z)-hexadecenoyl-CoA) and oleoyl-CoA ((9Z)-octadecenoyl-CoA) with higher desaturation activity on (9Z)-octadecenoyl-CoA than (9Z)-hexadecenoyl-CoA. Requires preexisting cis double bond at the Delta9 position of fatty acyls to be able to insert the Delta12 double bond. Delta12-desaturation of (9Z)-octadecenoyl-CoA in insects produces (9Z,12Z)-octadecadienoyl-CoA (linoleoyl-CoA) which may be used to supply precursors of crucial mediators of immunity and reproduction and other essential functions. Can also catalyze Delta9-desaturation on saturated fatty acyl substrates like palmitoyl-CoA (hexadecanoyl-CoA) but with lower efficiency