Keep a Xbow and arrows on you, mix scuba and riot gear. When tame gets shocked try to swim away and pelt with arrows. Only way I have managed to save my tames. Especially dangerous to squids. They get stuck in body much like anglers and mantas. Lvl health on all water tames. Will need it for your pet to survive long enough for you to rescue them. Of course try and avoid them at all costs. They will sneak up on you, and when they do heed the above advice. Good luck.
These are passive tames. In my experience trying to tame a 145. You will find having a Basilosaurus will provide you with a mount immune to the shock.
Wear a combination of Riot and Scuba gear. Bring multiple sets. They will destroy your tanks and flippers if you get hit enough times. Lone eels do not deal enough torpor to be a substantial threat with the riot gear.
The hard part is feeding them. They will glow bright blue (without goggles on) when they have built up a charge, and charge you. Discharge a 7 second stun, bite and then flee.
Lure them into an enclosed area. Such as a trap for water tames or a river. This will reduce their mobility and make them an easier tame than in the open ocean. Because they will flee the majority of the tame if they have the room to do so.
-Results of 3/20/17 taming test on Xbox official servers.