Here is a recipe to make your own ink. One of the ingredients is called 'Black lamp'. You can buy lamp black in a tube or make it by holding a plate over a lit candle. Dissolve the resulting blackener in a few drops of water.
To make 4 floz/115ml
1 egg yolk
1 teaspoon gum arabic
4 floz/115ml honey
1 teaspoon lamp black
Water to mix
Mix the egg yolk, gum arabic and honey in a small bowl. Add the lamp black, thinning with more water if necessary.