Water is what will cause your mayo to emulsify and become thick.
Sometimes folks get frustrated making mayo because it is not properly emulsifying and thickening up, and understandingly think that if they were to add more water, it would just be even thinner.
It is counter-intuitive. The extra TB or so of water (whether in the form of vinegar, lemon juice, mustard, or just water) is what will make it become a thick, stable emulsion.
If you are having trouble, try adding an extra TB of water to whatever mixture you were trying with before.