How Long is the Shelf Life of Refrigerated Eggless Mayonnaise

There is no rule of thumb encompassing all salad dressings.

One "rule of thumb" which sometimes gets used is to look at the shelf life of the most perishable component. Frequently it works; sometimes, it is dangerously misleading. A mixture of the things you listed can have a longer or shorter shelf life of that of the most perishable component. An example of lengthened shelf life is mayo; it stays good for longer time than a cracked fresh egg, because the yolk gets pasteurized and the pH is lower. But there can be examples of the other thing happening. The classic is the homemade garlic oil: you can keep pure garlic and pure oil for months in the pantry, but once you combine them, you get a botulism risk.

I don't usually keep salad dressings in the fridge, but if I did, I would look at why the most problematic component has the shelf life it has, and decide whether mixing it will change the condition. For example, if I had a mixture of oil, vinegar and pure emulsifier: Oil keeps for months because it has no carbs, so nothing for bacteria to eat. Vinegar can have a few carbs, but not a lot, and it also has a very low pH, so bacteria die in it. The combination still won't have enough carbs for bacteria, and will still have a low pH. So the mixture will keep for very long time, just like pure vinegar or oil.

On the other hand, imagine mixing vinegar with honey and water. Honey doesn't go bad by itself, because the carbs are too concentrated for bacteria. The vinegar and water will dilute them, so this mechanism of bacteria prevention vanishes. The pH of the mixture will probably rise a lot too, because the vinegar gets diluted, so no protection on that front either. Thus, this mixture is apt to go bad much earlier than pure vinegar or pure honey.

This method requires that you make a new decision for each new dressing you make, and that you acquire enough knowledge to be able to make such decisions. If you feel this is too much effort or too risky, you can either start adding conservants to your homemade dressings, or just start preparing a fresh dressing for each batch of salad.

To balance acidity, add sugar. It's how most mayonnaise manages to be acidic enough to prevent bacteria growth (pH 4.6 or lower), while still having a balanced and edible flavor.

You might get an edible result with honey, but sugar is more of a neutral flavor, so I would use that first. Using a jigger of Dijon mustard is not beyond the pale, as well... might help hide the acid, to a lesser extent.