Which syllable is stressed in the word "nineteen"?

The dictionaries list both possibilities to stress nineteen (or any other -teen, for that matter): ,nine-teen and nine-'teen.

Are the two pronunciations completely interchangeable, a matter of dialect, or a matter of meaning? I am asking because I've never heard nineteen stressed on the first syllable in sentences like:

I am nineteen years old.

He had only nineteen dollars.

And I have never heard nineteen stressed on the second syllable in dates:

He was born in nineteen sixty-four.

Is it acceptable (where, when?) to stress the first syllable in the first set of examples, and is it acceptable(where, when?) to stress the second syllable in the last example?

P.S. Surprisingly there's no stress tag. Am I using the wrong linguistic term?

All the number words for 13–19 are normally stressed on the first syllable (or none at all), but can be stressed on the second syllable for emphasis or contrast. It really depends on the sentence.

• I’ve got twelve. You’ve got thirˈteen. He’s got ˈfifteen.
• He’ll turn eighˈteen on his next birthday.
• I’ll shoot ˈeighteen holes today, not just ˈthirteen like last week.

If you were counting out a sequence, you would never stress the -teen portion:

• ˈseven, ˈeight, ˈnine, ˈten, eˈleven, ˈtwelve, ˈthirteen, ˈfourteen, ˈfifteen, ˈsixteen, ˈseventeen, ˈeighteen, ˈnineteen, ˈtwenty, twenty-ˈone, twenty-ˈtwo, ...

John Wells, formerly of University College London, highlights the phenomenon of variable stress:

There are plenty of words in English that seem to change their stress depending on the phonetic context. Typical examples are afternoon, unknown, sixteen. We say the 'late after'noon but an 'afternoon 'nap, 'quite un'known but an 'unknown as'sailant, 'just six'teen but 'sixteen 'people. The usual explanation of this is that the words in question are lexically double-stressed. Dictionaries show them with a secondary stress on the early syllable, a primary stress on the later one, thus for example /ˌɑːftəˈnuːn/ or àfternóon. I think that really the two stresses are of equal lexical status. The supposed difference between secondary and primary merely reflects the fact that when we say one of these words aloud, in isolation, the intonation nucleus necessarily goes on the last lexical stress, making it more prominent than the first.

I find his explanation fairly convincing. We generally don't quite like two stressed syllables together, and the stress shift in some of these words like nineteen certainly allows us to achieve this.