When I make my own Teriyaki sauce I don’t usually use the garlic and the ginger. I guess it depends on what I’m am going to use it with. I don’t think that Japanese people really use the garlic or the ginger.
There are a bunch of methods to prepare this glaze. The way I like to do it is combine soy sauce, Mirin, sake, sugar, (occasionally garlic and ginger) in a small saucepan and simmer down until 1/3 the liquid evaporates. The result is a fragrant, intensely flavored, syrupy liquid, with an undercurrent of garlic and ginger. You can also prepare this sauce without the garlic or ginger, or just use either/or.
You can of course use a thinner if you find its not thick enough for you. A tiny bit of cornstarch or arrowroot will work fine. Mine seems thick enough for me without. But I know some people want it thicker.
How to ruin your Teriyaki Sauce? Boiling down too hot and too fast. Be gentle, it will pay off.
How ti make your Teriyaki Sauce better. Make it the day before if you can.