If you want to do that, that you tear your tank apart to try and net the eel, you could if you want a mess of it.
In any event your a choice and no matter what, you be needing a load of patience for I guess this is a reef tank and I no idea to how well stock it be at this time.
Anyway, you can try a PVC pipe depending on the size of the eel you be needing twice the pipe and you can find some way to closed one end and I would have to think that using a net and rubberband would do well enough for you put a crab or shrimp to what it is your feeding this eel and place it at the closed end.
You then place this pipe trap as close to the eels lair and then from there it is a waiting game and if nothing happens one day, you try again the next but you have to be quick when the eel goes inside, but do not stay on top the tank, sit back and relax.
Give it time to go in that you can pull on the string that is near the open end and quickie, not rough like pull the pipe up to the water surface and then you caught your eel.
There are pipe traps designed that both ends could be closed up to catch your eel, I am sure that someone here would know how you can best do that.
Buddy