In Ellen Muth's speech I can hear basically all varieties: with the usual alveolar flap, with the seemingly elided t and with pretty pronounced glottal stops. Something I should be listening out for once I have time is when the ts are pre-vocalic and when not and what bearing that has on their pronunciation. The paper focuses on word-final pre-vocalic glottal stops, so the button phenomenon (phonemenon) probably won't be explained. Darn, now I have to go to the next lecture...
There is a Wikipedia article that seems quite interesting, but I don't know how viable it is to try and apply that to American English.
Another edit: I quickly listened to short sequences of Ellen Muth in of "The Young Girl and the Monsoon" (1999) and though there wasn't much time, I think I heard a few glottal stops at word-final pre-vocalic position.
There is something in this Mississippi business. Previously, you said there's elision in word-final /t/ generally and real glottal stops in words like 'button', which I would agree with. However, in the mp3 you provided, the speaker truncates word-final voiceless stops to such an extent that they really sound like glottal stops.
The other interesting aspect of the accent is that non-alveolar stops are truncated just as much as /t/, whereas (according to my ear) in General American the /t/ sounds more 'cut down' than the others.
I'm not a native speaker of course but my natural way of pronouncing "button" is to obstruct (or rather completely stop) the airflow at and around the alveolar ridge like when pronouncing /n/ from right after the /ʌ/ onwards which renders the rest of the word nasal, and I think there is also something glottal going on. When I pronounce it the way Ellen does—the Cockneyesque way—the airflow isn't obstructed on the height of the alveolar ridge until the /n/. (It is of course for the /b/ with the lips and then in the glottis.)
There is a transcription of someone from Mississippi here, who used a lot of glottalization, too. It isn't as special as it seemed to me at first, I guess. I'll probably try and add a few glottal ts to my speech if I should happen to have mental resources to spare. ^^
In General American many ts are pronounced as alveolar taps (/ɾ/) but that is not what I mean. I'll collect a few words as soon as I have a couple of minutes to spare. ^^
"Button" wasn't among the words I noticed but for "button" there is a mention in the glottal stop article.
I don't have much time right now but a few word are "thought", "doubt", "gotton" (same pattern as "button" I guess). Very often the ts at the end of words are missing but many of them seem elided rather than glottalized. Those three up there sounded very glottal to me though. And she already did that in the pilot, so she probably had the propensity before. Perhaps there are comprehensive books on American accents in one of my university's libraries.
I'm just listening to the commentary voice-over of the first season of Dead Like Me and noticed that Ellen Muth who is from Connecticut from time to time uses t-glottalization! That's so amazing! At that time on the set of Dead Like Me she has been working with Callum Blue who (at least there) uses consistent t-glottalization. Also the Wikipedia article says that even "Prince Harry frequently glottals his Ts". I can absolutely understand why that's so contagious. ;-) By the way, yarb, Dead Like Me was shot in Vancouver, BC.