My FIL lived in NJ/NYC area all his life when there was a deli on every corner in the neighborhoods. My FIL said this was the recipe used by all of them. Homemade mayo, chili sauce and relish were used then. But it's still great using the premade stuff.
NY Deli Dressing recipe
1 cup real mayo
1/4 cup Chili Sauce (comes in small bottle, like ketchup, it's not pepper hot)
1/8 cup Sweet Relish
Mix together and store in fridge.
For salads, sandwiches, condiment, or sauce.