lemon juice, or hot sauce. Worcestershire sauce provides a nice umami boost, too. Just remember the general ratio is one part horseradish to two parts ketchup (based on taste, of course).
a lemon peel, and horseradish. So what happened to all those varieties of ketchup? Tomatoes. The 1812 recipe from James Mease is the first appearance of tomatoes in ketchup. But wait, what about ...