Because eel is so thin, it will smoke very quickly. For this reason, try to keep the temperature of the smoker low and steady.
If your smoker has the ability to hang meats, tie a string around the head of the eel and hang the whole eel vertically. If your smoker isn’t set up this way, lay while eels (belly up) or fillets on a rack on a baking sheet. This will help smoke to reach all sides of the eel equally.