What is Tim's goal when he gets in his car and drives to northernmost point of Minnesota?

I think Tim is actually trying to get to Canada. He has been drafted to Vietnam and decides that he will flee to Canada rather than fighting in a war he does not believe in. Tim doesn't make it to Canada, he ends up at a broken old fishing resort in Rainy River. Thee he meets Elroy Berdahl, a quiet 81 year old man. Tim seems to come to his own conclusions over six days at the resort and ends up shipping off to Vietnam.