How to thicken garlic dressing
Actually, you can make an emulsion using just garlic and olive oil! It's a very old spanish recipe traditionally done by hand taking mind numbing time. 

Seeing that you want to achieve thickness using your existing ingredients (no cheating with emulsifiers) here is a suggestion that should work (i haven't done it, just seen it done).


Pay attention to the freshness of the garlics.  I believe the garlic oil may be a key here. So choose freshest garlic and don't go short.
Hold all of the oil for now and most of the vinegar, but enough vinegar so your mixer grabs and starts (you should have all garlic, and a bit of vinegar)
Run your mixer and add oil one drop at a time.
As the mixture thickens you can add more vinegar and more oil.  Lead with the vinegar as you're emulsion phase is oil in garlic/vinegar not the other way around.


It's possible that 1/20 time you immerse the blender into the vinegar first and pull in the oil slowly as opposed to whipping the oil and trying to bring garlic vinegar in.  If you're going for the fast method as you've been, pay attention to your initial blender depth and how much oil is trapped under the cap. 

Let us know how you make out!