I experimented with a ChatGPT suggestion of 35ml creme de peche and 5ml of noilly prat dry vermouth and it was a pleasant drink, unlike some of the other ChatGPT suggestions I've had the misfortune of trying!
Strange there are no cocktails with Madeira in them when I search for Madeira. I could've sworn I came across rainwater madeira in the book, but maybe it was another book I'm confusing it with.