I keep my eels on ice but if you hook an eel like that, while its easy, once it hits the water it comes right back to life and the tangles start. Here is what you do, grab the eel with a rag holding up near the head, whack the tail on a rock or whatever you have a few times, this will prevent the eel from tangling up your line, you want to break the spine about a quater of the way up the eel, this still gives the eel plenty of movement but no tangles. Cast it out and start a very slow retrieve just fast enough to keep tension on the line, make sure you reel the eel all the way in! many, many hits come in close as bass will follow it sometimes. Thats all there is to it.
For a shore bound angler , live eels will outfish any single other method there is, and they are availible all year! I know herring are good etc....but that doesnt last for consistant action use live eels.
I hook my eel different than most. Put the hook in the mouth and out the bottom of the throat.
As long as the eel is still alive it will work, I check mine by periodically pinching them near the head, if the tail curls a little its still fine to use.
As for the hit it feels like a bang or someone smacked your rod its unmistakable, sometimes its a light tap-tap, in either case drop the rod tip as soon as you feel this and let the fish run for an 8 count or so then pick up the slack and send the hook home! Sometimes you will get runs from small bass that will drop it, this happens and is normal, bigger fish dont drop the eel. During the 8 count I always feel the bass stop once and then move off again, at this point she is yours!
Everyone has different methods for fishing eels, this is what has worked for me for 20plus years.
Good luck! eels do work and you will hook up with them , just give it time.