Mauville City Gym especializes in Electric-type Pokemon. To reach the Gym leader, you have to change the direction of the electric beams by stepping on the colored switches with the same color.
Guitarist Kirk (Reward: p448)
Youngster Ben (Reward: p272)
Battle Girl Vivian (Reward: p608)
Guitarist Shawn (Reward: p476)
Gym Leader Wattson (Reward: p2,520)
Wattson will use Volt Switch regularly. Having a ground / rock-type Pokemon will help but won't be necessary to overcome Wattson's Pokemon. Bringing some Paralyze Heal will be a good idea too since some of his Pokemon's moves can inflict that status effect to your Pokemon.
After getting the Dynamo Badge, you can now use Rock Smash outside of battle and Pokemon up to LV40 will obey you. You'll also get TM72 Volt Switch from Wattson.
After clearing the Mauville City Gym, attempt to head north to find a couple of Team Aqua members. They'll mention once again that they need to go reach Mt. Chimney.