The Lightning Carrot is a pet-summoning item purchased from the Zoologist for 50 after completing 50% of the Bestiary. It summons a Volt Bunny pet that follows the player around.
When flying to keep pace with the player, the Volt Bunny emits a decent amount of light while moving erratically, which can spread light over an area. If there are no available tiles for the pet to "sit on" like when climbing walls or flying, the Volt Bunny will constantly jump around too.
The Volt Bunny is a reference to the iconic Pokémon character and mascot Pikachu, who is colored similarly and whose abilities revolve around electricity. Its animation while flying is also likely a reference to Pikachu's Quick Attack animation from the Super Smash Bros. series of games, sharing similar erratic movements and particle effects.
The tooltip is a play on the words "ecstatic" and "static", "ecstatic" being a synonym of "delighted" and "static" being an electrical charge.