I remember reading about cysteine back in 1983 as it was brought to the forefront by Durk Pearson and Sandy Shaw in their book Life Extension. Eggs are very high in this amino acid along with being a natural way to increase sulphur in you diet.
I would just add more eggs to your diet, as food is the best way in my opinion to increase the sulphur content. Buying directly from a local farmer is always best. The fatty acid ratio of the omega 6 to omega 3 is more apt to be closer to 1:1 The shells should be naturally thick and the yolks closer to an orange color. This is due to the natural diet of the bird which is insects, worms and greens and not loads of grains which are high in omega 6 but cheap to use as feed.
L-CYSTEINE - Amino acid peptide bond constructing up to 18% of your hair that provides strength, shine and structure. Cysteine increases hair shaft diameter and hair growth density. Foods high in Cysteine include eggs, muscle protein, garlic, onions, Brussells sprouts, broccoli, cauliflower, beans and milk. At least 500 mg. of this keratin-forming amino acid must be taken each day to even have an effect on hair. Cysteine is a powerful cell defender that acts as an antioxidant and also contains sulfur, known as nature's beauty mineral. A deficiency in sulfur is characterized by atrophied sebaceous glands which lubricate the scalp from the Essential Fatty Acids. Vitamin C in two and one-half times the amount of Cysteine, Vitamin B-6, and co-action of all 22 amino acids provide optimum use of L-Cysteine. In order for Cysteine to be effective it must synergistically work with ALL other aminos. A missing amino acid is like a missing building block that collapses the entire structure.