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The passenger's side T Top on my 80 Vett has stainless steel trim (shiny) that has been painted flat black. I can not adjust the window to line up correctly with the windshield pillar and the weatherstripping in the T Top. I suspect that I have an earlier T Top on the passenger's side and that that may be the trouble. There are other differences in the two tops. The driver's side T Top has gussets around the weatherstrip channel, the passenger's side does not. Does anyone know if/when they stopped putting stainless steel trim on T Tops?
78-82 tops are considered "single handle" tops, as there is just a single handle at the front of the top, and a pin that comes out the back, to secure it. The trim on the tops was stainless steel, painted black. 68-77 tops are all "double handle", with handles at the front and back of the top. The stainless trim was left natural on the earlier tops.
There were variations to the weatherstrip used over the years, and in mid 80, the way the headliners were attached, was changed. The shape size, etc. of the tops, was always the same, and any 68-82 to, should be interchangeable, if used with the corresponding rear mounting hardware.
I don't think the top itself, is your problem. I'd guess it's in the adjustment of the top or the glass, or possibly in the installation of the weatherstrip.