Yeah haha, I discussed it with my friends and we couldn't come up with a satisfying solution. But on further reflection, I think emoji reactions could be an option. Maybe the investigator would leave messages in different rooms representing the character running through the house, and the ghost has to react to the investigator's messages in sequence to "catch up". Or maybe the ghost can also write messages (or, realistically, a running emoji) and if the ghost leaves two messages in a row they "outrun" the investigator and thus catch them. Hmm...