How to thicken salad dressing
A very small amount of xanthan gum will work.  It is commonly used in salad dressings.  Be careful though, too much will result in an unpleasant texture that some describe as mucus-like.  Maybe start with 1/4 tsp. Wisk in and increase from there as necessary, but in very small amounts.  Xanthan takes a while to hydrate and thicken.  Start with a small amount, as the thickening power will increase with time.  You can always add more later.