Thank you all for your advice. For the time being I've requested the book about housebreaking the dog in 7 days from my local library. Hopefully it'll work for me. And, if needed for longer and find I think it is good, will buy it on the Kindle.
One of the other problems with this little guy's #2 habits is he is as quick as lightning. I'm not around him all the time, but when I have been around him and been able to catch him before he goes, it is a miracle to be able to catch him. Because when he decides to go, he doesn't sniff around hardly at all...and he is like I said, as quick as greased lightning. Incredibly difficult to catch before he actually does the deed. I mean, he's done before you've blinked, and generally doesn't circle or anything.
So, will give that method a try, unless some better ideas come along... I mean it'll be free

Thank you so much!
He's a wonderful little guy, and he is extremely devoted to me, in just 3 months. I certainly would not want to lose his companionship, as he is the best canine companion that I've ever had. And, just a beautiful specimen of Yorkie, with a very sweet temperament, and actually other than having trouble housebreaking, pretty obedient...even for someone who is a novice dog trainer, like myself.