Some old shows like "Our Miss Brooks" but I think others too, only listed the main actors, leaving out who played significant roles in an episode, even recurring roles. Some shows didn't list those parts, but did use voice over credits, e.g. "The part of the postman was played by..."
Did this have something to do with not wanting to create additional credit "cards" for each episode? I'm always going to IMDB, trying to find out who played a part, but sometimes they just seem to be lost to history, which is a shame.
Update: Sorry, Still trying to figure out the system here. Trying to comment overflowed. @Paulie_D thanks. I'm more interested in people not being credited at all. An example is the Brooks episode, "The English Test." The character Nora McGurk is important to the story, indeed she's in all of the pictures from the episode on IMDB, but the actress wasn't credited and IMDB doesn't ID her either.
The question you linked did give a possible clue: "Since the opening credits are pre-recorded, typically only season regulars make it into the "core" credits sequence ..."
That's what I was guessing. Only Eve Arden got an opening credit while Gale Gordon and the other 4-5 regulars got closing credits - presumably prerecorded as well. This may be why some shows used the voice over credits technique - to avoid filming new closing credits for each episode. That's my only guess. "Our Miss Brooks" just left those folks uncredited. I think there were some other shows that did that too, but I can't point to a specific example.