Equius made sure to show up early because honestly, he did not want to be there. There was the last place he ever wanted to be. Not because it was Tavros's birthday, exactly, that he was pretty ambivalent about, but because Gamzee fully intended to humiliate him in front of everyone everywhere.

He was sweating already.

Which was also why he was there so early. He wanted to be dressed and out of sight before anyone else got a chance to see him. At least, out of sight until "the moment."