I enjoy the movie so I think I can help. (also upvoted all your memes on the first page.) Rapunzel has hair that cures ailments. So thing to consider is mother Gothal suffers from old age. Note that she may be Abeloth after drinking from the fountain and succeeding. Either way she is ailing due to her age. So consider that Rapunzel is young or a child or an infant so needs no cure because nothing ails her except youth.
Also Gothal I believe must comb Rapunzel's hair whereupon it turns golden and bestows its life healing properties. This resembles Rumpelstiltskin using powers to weave straw into gold. The healing that Rapunzel requires for herself, say when she catches the flu and feels very awful? It is not clear how this is accomplished or I do not recall. It might be she tries NOT to brush her own hair.