If he's got plaque build up, it needs to be removed by the vet under anesthesia...no amount of teeth brushing is going to remove the calculus. If not removed, it can become a major problem, leading to gingivitis & periodontal disease. 1st dental cleaning done @ 2 years old is very common for Yorkies, esp if teeth brushing is not done everyday.
Feb is pet dental month, you might want to schedule for dental cleaning, vets offer a discount this month.
We had a discussion not too long ago about what to use for dental cleaning, a loofa glove was recommended. I got a pair from walmart for less than $2. Cut off the finger, put some doggy toothpaste on it & used it for Momo's back bottom teeth. It works better than gauze or baby terry cloth since it fits in my finger. Better than nothing! I use a tiny cat toothbrush by CET for his top back teeth, he lets me do that.
Virbac Animal Health — C.E.T.® Pet Toothbrush | United States
You can get it from your vet or online, like amazon.
My boys are scheduled to go in for their dental cleaning this Friday.