I doubt he's eating bristle worms. Cooked shrimp is no good. No bueno. Feed them raw. Strict sushi diet. I've never seen a grill underwater that had fire in it so the eels aren't putting another shrimp on the barbie.
Food selections for your eel include anything fresh and meaty that comes out of the ocean. Make sure there are no additives. Shrimp, krill, scallops, fish, oysters, muscles, octopus, squid. OMG eels go fool over octopus and squid.
If all that seems like too much work to hunt down, go to your LFS and buy a pack of LRS Chunky. If your LFS does not carry LRS tell them they need to, and go to one that does. That's all I feed my fish(fish and reef frenzy) and most of what my dwarf moray(chunky) gets.
Make sure the food is the right size. I've had my eel interested in food, but the size was too big and they quickly lost interest, even after I cut the food smaller. It should be no bigger than your eels mouth when open, but can be up to twice as long as their head(octopus or squid tentacles). They cannot open their mouths wide like some fish to inhale food. Instead they have a second jaw in their throat to pull food in. Think xenomorph from alien...
As far as eating on the 4th and 6th day, that's good. Young eels will want to eat more often than grown ones, but it isn't uncommon for them to go a few days to a week or two before wanting food again.
You also can tell when an eel is hungry. It has a look in its eye, a change in it's character. They go from being calm and nonchalant, to curious and inquisitive. Kind of like me when I smell food cooking. I want to follow the smell and see what's for dinner. So does the eel. Violent head shaking, is actually it's way of smelling. They have a very good sense of smell and they use that to hunt. When I thaw food for my eel, I pour just a little bit of the water into the tank and immediately he pokes his head out looking for dinner.
Go get you some raw sea food or LRS chunky and wait until you see the hunger signs. Then offer food again. Remember, eels may only eat once a month in the wild. A week not eating is fine.