In a pinch when out of tartar sauce I’ve mixed green relish with mayo and it’s, passable.
For that matter, mayo with hot sauce and ketchup was my accompaniment to some otherwise bland pizza and tater tots this afternoon.
Microwave Hollandaise sauce. Can go wrong easily, but when I wanted it quick it works fairly well. Just have to tend the microwave every 15-20 seconds to mix it before it coagulates. But it’s done its job more than once for me.
Equal parts soy sauce & water. Crushed black pepper, crushed hot pepper, grated ginger, sugar. Bring to boil, add ginger when off boil.
You can go extra with a crushed clove, 1 star anise petal to get some aromatics.
You can thicken it with a touch of rice flour or other flour.