There's a lot more than you would think. You see a dog that's good at "winding" a squirrel, there is a real good chance he has it in his back ground. Hog hunters round here breed it into their dogs for the same reason.
The true field bred bird dogs are bred to run. They hunt the field bred bird dogs off horses many times. If they stop running during the field trial, the dog gets picked up. Putting bird dog in your breeding puts winding ability and wheels on the dogs. They will flat hunt.
The very best squirrel treeing machine we ever had was 1/2 German Shorthair Pointer. Only problem we had with him was he hated skunks and would hunt them at night when able to get out of the pen. Kill them and come back to sleep under the truck. You knew quick, fast and in a hurry when he had gotten out and had a "good" night skunk hunting.
My GSP bird dog loves squirrels. I don't hunt birds but I do like squirrel hunting. I haven't taken her squirrel hunting yet . I fear that she would chase a deer into the next county. Maybe if I get a gps for my gsp , I will try her at hunting squirrels.