What is the technical description of the pronunciation of the "t" in "countdown"?

Solution 1:

Stops like [n, t, d] are said to consist of up to three phases: approach, closure, and release. And only the closure phase is essential. So the tongue tip need not leave the palate before or after /t/ in countdown and only voicing and nasality may change, and that's in fact the dominant pronunciation I believe.

It can be summed up in a diagram like this, which is often seen in a phonetics textbook:

                k aʊ n t d aʊ n

nasal passage   _/‾‾‾‾\___/‾‾‾‾

coronal closure ____/‾‾‾‾‾\__/‾

dorsal closure  ‾\_____________

voicing         _/‾‾‾‾\_/‾‾‾‾‾‾

In running speech /t/ may be voiced through assimilation (so that /td/ is realized as a long [d]) or elided completely. I don't think glottalization is common here given the /t/ is surrounded by voiced alveolar stops, leaving little motivation for glottalization (in other words, it doesn't ease the articulation). But I could be mistaken.