I believe the more normal system for drag hunts is they drag an appropriately smelly bag around, leaving a trail for the fox to follow. Typically fish - I think that fish has traditionally been used, hence the expression "Red Herring".

Chasing a jogger sounds more fun. But you can imagine it might be a bit nerve-racking as the hounds catch up - you'd be worried the hounds might turn out to be traditionally minded. "Now that's a bloody funny looking fox! Still, now we've caught the bugger, we'd best tear him limb from limb."

Sid Kipper suggests a variation in which the hounds chase Morris Dancers, more specifically the ones who dress up in drag.