Mix sausage, salt, pepper, cayenne pepper, dried sage, fresh sage, pistachios, and apricots together in a mixing bowl with a fork until just combined. Divide into 4 portions and shape into patties about 3/4 inch thick.
Cut caul fat into pieces about 2 or 3 inches larger than the crepinette patty. Wrap patty in the caul fat with ends tucked on the bottom. Patties need to be completely covered. If your caul fat pieces are small, you can overlap to completely cover each patty. Trim any excess caul fat, if desired. Place patties on a plate and cover with plastic wrap; refrigerate overnight.
Heat 1 tablespoon oil in a skillet over medium heat. Place crepinettes smooth side down in pan. Let brown 3 or 4 minutes on each side. Blot some of the rendered fat with a wadded up paper towel. Pour in a splash of white wine; cover. Cook covered until interior of patties reaches a temperature of 145 degrees F (63 degrees C), or another 5 minutes. Uncover and turn crepinettes to coat with the pan brownings and to reduce some of the wine.