Cut the animal fat into 1-inch cubes.
Pile the cubes in a large pot. Add just enough water to cover the cubes. Bring to a boil, then immediately reduce the heat to a simmer. Allow to simmer for at least one hour.
Strain the separated fat into a bowl to get rid of any bits of meat.
Cool the contents of the bowl to room temperature. Place the bowl in the refrigerator overnight.
Lift the hardened fat out of the bowl. There will be liquid left behind in the bowl to discard.
Fill the pot with water. Break up the fat and place in a pan. Place the pan on top of the pot to form a double boiler. Heat the water gently until the fat melts.
Cool slightly. Poor the warm fat through a mesh strainer, funneling into a Mason jar. Pour the strained fat back into the bowl. Allow it to come to room temperature, refrigerate over night.
Break up the tallow and place back in the double boiler. Pour sunflower oil into the pan until the tarrow is covered. Heat gently, stirring to incorporate the fat with the oil.
Funnel back into the Mason jar. Allow the mixture to come to room temperature at which point it should be in a gel consistency. Pour the gel into the oil lamp.