Alright, I got it figured out now. The threads on this particular bottle neck/cap are 23.5 mm in diameter and 6 mm in pitch, three 1/2 revolutions, spaced 120 degrees apart. I started the thread pattern 1.5 mm in from the edge of the cap that I made. I came up with this by measuring the threads on the bottle neck since I don't really have a way to cut one of the caps in half to take measurements from a cross section, although this would be the preferred method. Thanks for the help and input!
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