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.
I find gravy to be one of the easiest sauces to do quickly and with whatever I have on hand (1:1:8 ratio for fat, flour and liquid).
I made a brown sauce for poutine and some other potato dishes kind of like this the other day: melt butter at medium low heat in a small pot, say about 2 tbsp, add equal amount of flour by volume and fry until getting a little nutty. Whisk in broth or stock (I just use Better Than Bouillon) until consistency of thin gravy achieved (about a cup) and it begins to bubble. Add light and dark soy sauces for flavour and colour to taste. It’ll thicken as it cools.