I have followed other cases where scent (tracking, not cadaver or human remains detection) dogs were used to look for a missing person who may have left on foot. What I learned from those cases was extremely interesting. We had some search and rescue experts posting at that time on those cases. These people were expert dog handlers and knew just about everything there is to know about how dogs track people, either dead or alive.
The experts told us that a person who is depressed or suicidal may give off a different scent than when they are not in a depressed or suicidal state. Humans would not be able to notice such a subtle difference in body chemistry or the person's scent, but to a trained search and rescue dog, there would be a different scent.
The way it was explained to me was that if the scent article provided to the dog was a shirt or a towel or something that the missing person had at the home, the dog would be trying to track that scent. However, if the missing person left on foot in a suicidal or depressed state, the scent wouldn't "match" the scent article the dog was tracking and the dog would not be able to to find a trail for the missing person.
I hope that makes sense. Maybe a verified search and rescue expert will join us here to further explain the science behind this.
And for the record, I obviously don't know if Tim left on foot or if he was depressed or suicidal when he left, since he has not been found, but I have been thinking about the dogs and if that's why they haven't found a trail for him, if they haven't.