Movie about a man that thinks he’s a driver/car

On the edge of giving up on this movie. I’ve been trying to find it for years, and now I’m here. Hope that somebody can answer my question. I can’t say I remember much of it as I watched it when I was a little kid, but this is what I remember. It’s an older movie. I’d say 80s or 90s. There was this man that I think was suffering from some mental illness, and he was pretending to be “driving” an invisible car. He would hold his hands up front as he would hold a steering wheel when he was “driving”. There was a scene where he raced another guy on a horse and I think he outruns him. Also, there was this fraternity house I think. Beta/delta/alpha something. Thanks in advance!