So many times eels will come in with pre-existing conditions and at a few months is when sometimes these conditions can appear. You may be feeding too frequently unless he is an itty bitty guy, most zebra's come in at a pretty good size, so a couple times a week at most, an adult more like once a week. Large adult zebra's even every 10 days. Depending on what pieces he is getting from the lrs, a variety including a fish like SFB silversides or even occasionally some salmon. Scallops are good, even mussels and clams. Shrimp should be whole with any sharp edges of the shells removed. Your diet wouldn't negatively effect him that quickly. What is your mg, mg is important to digestion, at least reef level I'm sure, but you can elevate safely to 1600ppm, I keep my pred tanks at 1400.
As far as pre-existing conditions, the most common would be internal organ damage due to chemical exposure, and yes, that does include copper. If he came from a lfs that runs copper or you used copper in your qt or treated with copper. Some argument can be made for other meds as well, anything with formalin or formalin derivatives definitely, and even antibiotics. Tank cleaners or pest eradicators can have a negative effect. Cyanide is also back with a vengeance. Eels natural metabolism process toxins at a slower rate, making them more toxic to organs like the liver, which is responsible for eliminating toxins. Eels can handle pretty high nitrates, if your other fish and corals are not effected, then the eel could care less, especially your gem tang would let you know if there was a problem with water quality.
What I would do. Raise mg to where you feel comfortable, as I stated earlier, I have found 1600ppm to be safe and has helped some of my preds with digestive issues. He could be getting some bloat or blockage from too frequent feeding. Let him go a solid week without food and start offering him a variety, then cut back a bit on the frequency of feeding. There's no real diagnosis to offer a treatment and it is very unlikely he would have a disease to spread to the rest of the tank, so no real need to move him. At this point all you can do is hope for the best, there is no remedy for chemical poisoning, but many new eels will develop a digestive issue which is easy to remedy.