My personal bet is that until the bechdel pass rate goes up into ~90%, your point won’t really fly and the reverse will be passed all of the time … still interesting to find out.
In the era of “just asking questions”, I certainly understand any implicit assumptions that I’m oh-so-cleverly concealing some ill-conceived “point” about feminism. Certainly a case can be raised that by presenting a possible chink in the supporting evidence of your post is an inherently disruptive and destructive act; clearly your broader point about closet bigotry affecting fan biases is both correct and worth emphasizing. I’d far rather strengthen your argument than tear it down. I hope that’s ultimately what I’m doing here.
Given the numbers and the low bar of the Bechdel, some quick sampling could probably be done to get a picture. Select 10 episodes that pass the Bechdel test and 10 that fail, maybe some from TNG ans some from voyager, and we here collectively try to see if they pass/fail the reverse bechdel test in a group effort?
I don’t think I would trust the results of this, unfortunately, as there’s probably a reverse correlation between the Bechdel and reverse Bechdel tests; in a sample this small that would pollute the results. For example, take any episode where two characters of the same sex are stuck together in some sort of trouble. That episode will surely pass one of the tests (Bechdel for two women, reverse for two men) but has an increased chance of failing the other because much of the dialogue for the rest of the characters is likely to revolve around the plight of the imperiled pair.
…which isn’t to say that what you suggest isn’t worth the attempt. Certainly raising an issue and then shooting down a proposed solution to it isn’t very helpful. Episode transcripts are out there; maybe there’s a software solution here? Automatic identification of conversations between two characters would be imperfect but manageable, running that dialogue up against a list of names of male/female characters and then manually checking up on the episodes that missed to avoid false negatives would probably be the most technically efficient way about this?
Circling back on your actual point, though… You are absolutely and unambiguously correct that TOS did a horrible job with gender representation, much worse than TNG did (or could have been expected to by fans when it was about to air). It’s also clear that Voyager did much better than it’s contemporaries, and ENT was a pretty harsh step backwards. You don’t need to know the base rate to establish if one number is bigger than the other, only to draw more nebulous, general conclusions about how well shows are doing with gender representation.