Very true there are curs in every litter .. But you would have a much better chance at finding a pup off parent's who are proven hunters and bred for that purpose vs just taking any random dog that has not been bred for performance work. You can wave a rat in front of a dog all day long if they don't have deep intense prey drive levels that hunting dogs possess they will not stay focused on going in for the kill. Part of the focus your dog is lacking for it's prey is tied into the fact your dogs prey drive levels are low to begin with. When a dog has high levels of prey drive nothing can stop the dog from going after what it wants and it will ALWAYS give 100% of it's attention to it's prey.
Exactly, also i might point out its not called a game dog, what your aiming for is a catch dog. A hunting dog.
As sadie pointed out they either have it or they dont. Being trained is one thing however when a dog lacks prey drive and courage (this is needed to a certain extent depending on what your using them for) the end result is going to be the same as a never trained dog. Other types of traits/drives that can be beneficial is fight and pack drives.
Prey drive should be obvious as to why its needed.. and as sadie already pointed out if a dog lacks the drive and determination to chase and kill its prey than the dog is hopeless when it comes to hunting.
Courage and fight traits/drives are also highly important if you are looking for larger game prey. These are also traits that will be beneficial if you are talking about hunting an animal that can cause real harm/threat, especially if your talking 1 - 1. (no pack) Prey drive might not be enough if the dog becomes wounded during the catch. Generally, these are on the bottom end of whats needed but again it can benefit the dog greatly if we are talking about larger game.
Pack drives should also be fairly obvious. If your looking to hunt with a pack of dogs, the pack mentality needs to come with the dogs. A pack of dogs more willing to fight each other vs catch the prey are going to prove to be useless in other words. Of course, this isn't a needed trait only if it suits the surroundings and goals. (no pack/pack etc)
If you feel your dog could be suitable for hunting feel free to PM me, i can get you in the right direction however i would recommend given lack of experience, etc you speak and get with seasoned hunters that use dogs. This will greatly benefit the training aspect and learning aspect. It can also benefit you when it comes to hunting with new game if already seasoned.
I know you say thats what your dog is based on location however if that is really what your working with, i don't believe your dogs genetic make up will work out for the work.