I, too, am a big fan of this sauce. I'm forever heading off to the late-night falafel stand to get a garlic sauce fix. I did once try to aproximate the food there at home. I'm purely a novice but I thought it came out tasty enough. I made the sauce just like a mayonaise... which is why I asked about the absence of egg. One expects that an egg-less sauce would keep longer. What I ended up with was an aioli, but with lots more garlic (an insane amount of garlic). The local falafel stands serve the garlic sauce on their beef and chicken sandwiches, and also on their "garlic potatoes" which I also tried to aproximate with mixed results: tasty, but not quite like I get at the resto. Home-fried style potato chunks cooked with (agian) lots of garlic, a little cayanne pepper, salt and black tea.
Hmmm... I think I need to go get a falafel,