Someone pointed me to this video which shows someone repairing a TriMark latch unit. I think it is just what I was looking for and I'm putting it here in case someone else is wondering about the interior of this latch.
https://www.youtube.com/watch?v=Epq8MrrRF7c
About 1 minute into the video, it shows the little white plastic piece and where it goes. That is the main thing I was trying to figure out as I believe it is what is supposed to keep the springy latch from extending too far (and thus making it so the door won't close without assistance). I'm going to check it out on my latch later today to see if I can get that piece to fit in the right place. I'll report back...
-Chris
