Naturally, his first instinct wasn't to steal himself and fight so he could escape or defeat August. His first instinct was to use any means possible to get the other genius away from him.
"Come out!"
He screamed in a panic as he backed away.
August was already turning to look at him again. He was purposefully moving slowly so that Wilhelm could observe the intent behind his every action. Perhaps it was a way to taunt or torture him, but it actually worked in Wilhelm's favor.
He discovered that August was still alive through a certain source in another Holy Clan. The information was planted for an unknown reason, but once Wilhelm confirmed it with his own people, he immediately made a plan.
Rather than telling his elders so they could send someone who was overqualified to kill August, he wanted to do it himself and earn the glory.