Ah, the T-top. Like the opera window a classic from (mostly) the 1970s. This semi-convertible feature was designed to give you the open-top experience of a convertible while getting rid of flimsy and leak-prone rag-tops, giving the driver a coupe-like quiet inside and maintaining some semblance of structural rigidity. Pop the panels off, stow 'em in the trunk (or garage if the rain chance is low), and you can cruise around admiring the sky and feeling the wind in your hair.
That was the idea anyway. What many ended up with was a leak-prone roof that didn't make much appreciable difference in what was considered 'handling' back then. Whether installed at the factory as part of the options package or put in later, T-tops seemed like such a great idea but never really worked as well as their billing suggested. They've made an appearance off and on since their heyday in the 1970s, but for the most part they've been supplanted by traditional convertible tops (that actually work well), single-piece removable tops (ala, the modern Thunderbird), or more modern retractable hardtops.
I've often thought that the T-top was a great idea -- a happy medium between the true convertible and the coupe -- that manufacturers would find some way to bring them back, make them work well, and give us nostalgia-seekers a little feeling of semi-convertiblism in our modern, comfortable, and well-performing automobiles. It's been 30+ years, the time must be ripe. . . .right?
Probably not, sadly.