A homocercal tail is a caudal fin composed of two lobes of equal proportion.  Homocercal tails are the most common caudal fin type in fish but can come in many symmetrical shapes.  A homocercal tail is contrasted with a heterocercal tail which has unequal lobes. (fishionary.fisheries.org/homocercal)

The Rose Fish has an even-lobed homocercal tail.