How many other fish are in the tank and are they showing any signs? I would definitely rule out stray voltage first as others have mentioned.
If you have a good magnifying glass or better yet, a macro lens, take a look at your tang's body and eyes. If the tang has body flukes, you may be able to see them, especially if they are on the eyes.
The symptoms for flukes are similar to ich, but you won't see "salt crystals" on the fishes body. You may see mucous. The fish will flash and scratch on rocks and sand bed and their breathing is usually labored and rapid. Flukes will not go away on their own and without treatment a fish will die. If your tang has them, the rest of your fish will need to be treated as well.
They can easily be treated with Prazipro and it can be administered in a DT if necessary, although a QT environment is easier. I have dosed it in our reef without any issues other than a few corals (birds nests, stylophora) browning out a bit. They colored back up w/in a month after treatment. If I remember correctly, there are a few soft corals that may be affected by the treatment such as Xenia - I'm sure some other folks can chime in. If you decide to treat your DT, make sure you follow the instructions.
-Terry