Interesting. We too have an 8 month old Westie but I certainly wouldn't say a trait of Westie's is barking, at least not in our experience. He does bark territorially (someone walks by front door, back yard, hears another dog bark when at home) but that is it, not a peep at any other time, even during play or for attention.
We did teach our Westie the "Quiet" command for when he gets a little too territorial and won't stop barking after hearing another dog bark. It's pretty simple to teach and may help with the TV.
You need to find something that makes him bark (You have a TV!). Make him bark and then the second he stops barking, even if for a second, give him a treat (I'm a big fan of clicker training so if you do use a clicker, click then treat, otherwise say "Good" then treat). Next time, he has to stay quiet for 3 seconds, again, click then treat. Work up gradually until he stays quiet for longer periods, 10 seconds, 30 seconds, a minute.
Once he understands that being quiet gets him a treat, introduce the word "Quiet". Now before clicking or saying "Good", say "Quiet", click then treat. He will learn to associate "Quiet" with being quiet. Again build up the time after you say quiet and he remains quiet, before giving him the treat.
All training for puppies is basically the same. Wait for them to do what you want, and reward them for it. They will understand soon that doing that thing gets a treat. Then you teach them to associate a certain word with what they are already doing, in this case, "Quiet". Do not start off by saying quiet as it means nothing to him.
Eventually, he will actually learn that the TV being on is a signal for him to be quiet. He will actually purposefully become quiet in hope of getting a treat. A lot of people teach similar things to their dog for the door bell. They teach their dog that when the bell goes, the dog has to go and lie on his mat. You are essentially doing the same, teaching him that when the TV is on, he has to be quiet.
We taught our Westie quiet early and perhaps that is part of the reason he doesn't bark at anything other than territorial guarding (I don't think anyone can stop that in a Westie!) He also does go quiet when we tell him to be quiet, although it's not as solid as we would like (he sometimes starts up again shortly after).
FYI our Westie does bark at the TV but ONLY when he see's or hears another dog, which I again suspect is territorial, never at random noises or animals etc.