I've never had to chase one either. whether usin a shotgun or bow. I shoot for the base of the neck when usin a shotgun, and try to hit through the wing and into the top of the leg when bowhuntin. with his legs out of pocket, he can't run, and he can't fly, becasuse he has to have his legs to get airborne.
but it's always a good thing to get to the turkey as quick as possible. him floppin around like that he can lose tail feathers which he needs if your goin to make a fan mount.