My favorite type of hunting is flushing, I work the hedgerows, thickets, and brush piles. No telling what is going to pop out of there, Pheasant, Hare, Fox, Coon or whatever. Two approaches, a good nose dog or a naturally busy dog. I have a Plummer Terrier now, good nose, an active hunter, aggressive, a real go-getter. Hunting drive and aggression are usually two things you can't teach, but you can encourage them. My Plummer will eat Hedgehogs if I let him.
A lot of game will dig in and hide hoping you will pass them by. IMO for every game animal, you see there is at least one other close by that is hiding, often more than one.
The beast Squirrel dog I ever had was of all things a German Shepard, he was also a good Rabbit dog. My philosophy has always been to figure out what your dog is good at and hunt that, instead of trying to diligently train a dog to hunt what YOU want. Heck I'm flexible. Most dogs are born with a set of talents and urges, why not adapt?
I have another dog that is half Jack Russel and half Plummer. She is a born earth dog and will head down any available burrow. She was born with the urge.