GWBrown,
Separate the two, it is really not fair to the cat that has lived there for 13 years. 

I'm sorry and I don't mean to be harsh but if you "have to cover the dog's eyes to get her attention" you have a serious problem already.  That type of approach and mentality is going to cause you lots of problems training this dog.  You need to take control of this situation and fast.  Covering the eyes of the dog to get it's attention is not doing anything.  Be firm, very firm and strong and make the dog focus on you. 

I agree with putting a leash on the dog and trying treats, I doubt that will be effective.  However, I would put a leash on the dog and correct strongly and end this behavior immediately if the dog goes after the cat or even thinks about going after the cat.  The correction needs to be strong enough that the dog never wants to chase that cat again for the rest of it's life for fear of another correction.  If you do not have the ability, skill or intestinal fortitude to deliver an effective correction you may need to find a new home for this dog.  My intention is not to offend or insult you, but express the reality of the situation. 

I would never leave the dog and cat alone together, the dog will more than likely kill the cat.  It is fairly easy for a dog to kill a cat, especially a cat that is 13 years old. 
 

Jim


 

I don't know if there is anything in my experience of this area that will be helpful, but on the chance that something might be useful - and anyway to show a glimmer of hope generally on this topic - here's what i once did: Had to bring a 3 1/2 yr old bitch to live with a 13 yr old cat. Bitch was not particularly cat-friendly or experienced. Her mother & grandmother were cat chasers.The cat had never lived with a dog before, but was a strong character and had been known to 'face down' dogs outside my flat.  I got a big crate and put the GSD straight in it, so cat was free to walk around and pass her but she could not get at him.  Things that others have said about give the cat lots of high-level bolt holes, work the dog while its out on walks etc to wear it out, concentrate on teaching a solid Leave, all apply, as do first meetings on lead, never leave them together unsupervised.  Within two weeks she had given up trying to get at or chase the cat; within a month they were absolutely civil to each other under all circumstances.  They never became best friends as in curling up to sleep beside each other, but they were always fine in every other way. He died at 17, she clearly missed him. She lived to 14 but I never had the opportunity to get another cat so don't know how that would have gone.  One thing I did which may not go down too well with the "never say No" brigade - the cat was always 2nd in my household, the dog definitely 3rd. Cat always ate after me but before her;  could sit on the furniture, which she was never allowed to do; generally held up to be superior to the dog. I feel this approach helped greatly.
 

A lot depends on the dog. I had a female that helped me raise a litter of kittens. I currently have a male that tried to kill my cat the first time they met. Eventually, they became best friends, and he very clearly missed the cat when it was run over by a car.

However, if your dog has really high prey drive, it may not work out. I have several friends who have to always keep the cats separate, and one friend who thought things were working out, until the cat had to spend a few days at the vet's. When it came home, it smelled strange, and was no longer accepted by the pack. They tore it to pieces while the owner was at work.