I found another video of the door deploying automatically. "The Battle" 01:03. However, in that case McFadden appears to be molding the door closed with her finger rather than using the latch before she lets it go.
I was hoping to do something more durable, just because it would be an interesting challenge and potentially a satisfying result. The originals were probably rigged up in a similar way to what you describe, which is perhaps why they didn't survive much beyond the first few episodes. =\
I can't quite tell from the photos what the set up is there on the bottom door. I think it's a piece of brass hardware like a rod or bar, but I may just be biased by replicas I've seen that have done it that way. It's hard to tell from the actual captures. For all I know for sure, it might as well be the very fishing line you propose. If it's a solid piece of metal, I'm having trouble envisioning it having the necessary clearance inside of the body unless the hardware itself were hinged somehow. Maybe I need to try to model it somehow before I'll understand the viable options.
Are you talking about the ratchet sound itself? I think that is just inherent to the motor releasing its tension.
Or if you're talking about the single louder click we hear when the door is closed shut (from the spring-loaded lock pin popping into its hole)? I don't think we need a click sound as the door opens, do we? I don't hear one in "Home Soil." It's possible the post-processing sound effect with the ratchet and click was applied to both door opens and closes later on, but I don't think it's there in the early episodes.
I previously haven't paid enough attention to tricorder appearances since I figured most all of this info was already known, so I'm catching up a bit. I'm going to see if I can dig up any production photos or info from those early days beyond what see see in screen caps.
Yes, on the ones I have if it's not wound super tight, the rotation is actually surprisingly slow—perfect, I would think, to match the Data door deploy scenes from Season 1.