There are differences in accent between age groups, but these are not as great as the differences between individuals of the same age. And "General American" is a spectrum of accents from a wide area of America (from the West, Northern Mid-west, and parts of New England). It is not truly a single accent. Moreover, most people will be able to "code switch", and change their accent. It's all subtle, complex, and learners really don't need to worry about it because you can be understood even with an accent.
You should try to find your own voice, using several different models. You should not restrict yourself to people of a single age/gender/race/region/social-class. Native speakers don't learn by only listening to one person!
If are talking about "the accent spoken by people on American TV shows", there are a whole range of accents. Many are in the "General American" spectrum. But there are lots of variation and many who are not General American if you listen carefully.
So don't worry about age.
Your bigger problem is not having people to interact with. Listening is useful, but unless you are speaking and being understood, you can't practice your accent.