In a pan, combine all ingredients over medium low heat.
Reduce by about three-quarters, beginning to taste it about halfway through the reduction. It should be full-flavored and sweet and tangy.
Strain mixture and use.
To use: brush on the unagi, broiling the unagi in oven or grilling it.
You can also let the mixture cool, and store the glaze in a clean bottle in the fridge.
Here are the actual instructions Chef gave me, in his wording: "Unagi glaze is very simple. Just reduce bottled terriyaki sauce with a 1/2 cup of brown sugar and 1/4 cup of rice wine vinegar. Add some chopped up ginger. Reduce this by about three quarters. Start tasting around halfway. It should be full-flavored and sweet and tangy. Strain and brush on the Unagi under the broiler, or on the grill".