The Legendaries and Their Role:
Thunder and Lightning:
Representing summer storms, it based off Native American thunderbird. It represents the harshness of summer storms in certain regions like America and India.
Representing descended lightning, Raikou is based off tiger form of raiju. It represents the force of lightning impact onto ground.
Its Incarnate Form is based off Raijin, Japanese Thunder God that uses drums create thunder to summon lightning. Its Therian Forme is seemingly based off Azure Dragon, which is traditionally not associated with thunder, except in Digimon(Azulongmon) and some SMT games(Seiryu).
Tapu Koko is based off Kūkaʻilimoku, Hawaiian God of War, and represents conflict. It collects lightning to empower itself and disturb others.
Zekrom's tail is based on a jet turbine, though its looks more like a generator. This is likely meant t symbolize idea creation and thought process.
The Trainers and Their Roles:
"The Lightning American", who was once a pilot in the "war"(believed to be Vietnam War), he uses his old survivalist tactics to convert his Gym into a stronghold. Despite this, he likes kawaii Pokémon.
Founder of Mauville City and New Mauville, as well as original project leader of Sea Mauville and the implied leader of Devon's Infinity Energy research he is called "The cheerfully electrifying man!".
"The Shining, Shocking Star", he is a friend of E4 Flint. He built his Gym puzzle because he was bored. He has J-Rock aesthetic, despite being unrelated to that. He is currently the strongest of Electric-type specialists.
Though she is not an engineer herself, she uses machines as part of her clothing. Her nickname is "The Shining Beauty"
Called the "The inventor lighting up the world." he is a child genius that created Super Training. He is basically an unathletic nerd.
One of the Trial Captains, he serves as the in-universe explanation for Festival Plaza, as its creator. He is based off a weeaboo, basically.
The Overview:Virtually all Legendaries are associated with thunder and lightning one way or the other. There is no escaping it, because it is the most common form of electricity in nature, and mythology. There hasn't been a more abstract apostasis that represent electric charge, positive and negative charges, magnetism etc.
Similarly, virtually all electric trainers are associated with engineering, either due to interest(Volkner), association(Lt. Surge), fashion(Elesa) or their actual role(Wattson, Clemont, Sophocles). Elesa and Lt. Surge at least showcase Electric-type in slightly different contexts, in fashion and in military inspired species.
Despite its abundance in roles, Electricity would require more mascot legendaries and possibly an Elite Four and Champion to fully complete itself. It is still a far too rare type to fully develop. And of course a proper Electric-type villain team would also help.