I actually made a batch of Harvey's Sauce, tonight. I found it as an ingredient in a recipe I wanted to try, from a cookbook focused on South African food from 1914.
It looks like the recipes for Harvey's Sauce replicas, over the years, were designed to approximate the original flavors without things like walnut ketchup and mushroom ketchup. I researched several of the replica recipes as well as ingredients from walnut and mushroom ketchups. I didn't want to go to the store so I did make a few substitutions.
About 1/2 cup apple cider vinegar
About 1/2 cup brown sugar
About 1/4 cup water
1 T tamari sauce plus 1 T jaggery sugar to approximate India Soy Sauce
1.5 t fish sauce to approximate the 3 anchovies because I had none at the time
1 T tamarind paste
1 t ground mustard seed
1/2 t ground ginger
1/2 t ground cloves
1/2 t ground cinnamon
1/2 t ground allspice
1/2 t urfa bieber pepper (as a sub for cayenne pepper)
1/8 cup grated onion (maybe a little less)
2 large garlic cloves, crushed
1/4 t salt (not iodized)
1/4 t smoked black pepper, freshy ground
1 T lemon juice
1/4 t Trader Joe's mushroom and company seasoning (to approximate the mushroom flavor)
Just cooked it all in a pot. Let it cool. Put it in a jar. It doesn't make much. It will easily be gone before it gets too old.
It's sweeter that Worcestershire sauce, much more complex than modern ketchup, way better than A-1, and more interesting than anchovy sauces. The text time, I want to use anchovies. Or possibly increase fish sauce if I do the substitution.