Here is another possible alternative.....this one posted by Suzin....perhaps on this website.
1/2 cup oil
1/2 cup water
1 Tablespoon apple cider vinegar
1 Tablespoon lemon juice
1/4 teaspoon dry mustard powder
1/2 teaspoon sugar
1/2 teaspoon salt
1 teaspoon sweet rice flour
1/2 teaspoon xanthan gum
Put all ingredients in a blender jar and blend for about 3 minutes. This is a basic recipe....I usually add some seasonings....1/2 teaspoon garlic powder, 1/2 teaspoon onion powder, 1 teaspoon parsley flakes and a small pinch cayenne to make it a ranch dressing but you can add any seasoning you like. This keeps well in the frig, about 2 weeks.
Yes, I've seen this one (or something very much the same) on this forum before, and the sweet potato flour would of course also need to be cooked first. It's not a big deal to do, but it seems to be left out of the directions most of the time. A raw flour/starch simply doesn't thicken nearly as much as a cooked one. Incidentally, from all my experiments with making mayo, lemon juice makes for a stiffer result than vinegar, but of course there is a difference in taste. Some brands of mayo use one of these, while others use both.