Xanthan gum - this is the same thing used in commercial salad dressing. You can buy it on Amazon or at some natural food stores (some people use it for gluten-free recipes). It is pretty simple to work with, just blend it into a liquid, no heating required.
nothing...even high processed vinegarettes like Kraft separate..cruise the salad dressing aisle at the supermarket and check it out. in order for it to not separate you would need to emulsify it and then it's not really a vinegarette anymore, it's an aoli or flavored mayonaise or some sort of odd mix.
Once you emulsify it, it becomes a.....(drum roll please) Emulsion.
If you want an emulsion without the gums and starches, use a natural starch: Over cooked rice (NOT Unkle Bens) Toss in a handfull of overcooked rice and the vinegar/acid you want to use into a blender, then add in your oil.
Of course, you could also use egg yolks.......................
To be seriously technical..even just oil and vinegar properly mixed is an emulsion..however they will separate eventually, in either hours or just a day, it's inevitable. Even with chemical or natural emulsifiers it is going to happen it's just a matter of time. The old adage "oil and water don't mix" is a time tested scientific fact and feel free to add vinegar to the water list at this point. Stop screwing with it, please.
My understanding is that any thing used as a binding agent is exactly that. They do not chemically combine the molecules but rather trap the molecules, hence acidity, sheer and temperature all speed up or slow down the process of separation, as Gunnar has pointed out oil and water don't mix...forever
there are broken vinaigrettes and emulsified vinaigrettes. it's still a vinaigrette. a sauce that is bound with eggs (due to the lecithin in the eggs) is no longer a vinaigrette, but a mayonnaise or a derivative of. ie: caesar dressing is not a vinaigrette.
just because a vinaigrette is emulsified does not make it a mayonnaise. "aioli" is neither, technically.
a vinaigrette is a temporary emulsion whereas a mayonnaise is a permanent emulsion.
any further reference can be found in McGee's book or even J Peterson's "sauces" or "glorious french food".
to the OP.... do a search for "fat emulsifiers" or "emulsification stabilizers" to look for other avenues regarding lecithin or gums.