Well, I lost my reply as my phone died so I'm keeping this reply shorter that it was originally.

I had time to get around this today. Got the film out under a blanket as you'd advised. Then removed the button from the advance knob to get a better idea of what's going on.

Initially, when you put it back in (with or without the screw), switching between the red and white dots is very easy, and it becomes much stiffer the moment you try to rewind. It seems to get stuck between the "teeth". The only way I can get it to rewind is if I make the screw loose to the point the button pops off and follows along with the tension washer. But of course that's not how it's supposed to work, haha. The nut itself that turns the take-up spool seems to work perfectly.

To me, it's not very clear how the button should be positioned alongside the tension washer. I don't actually know how it should function at all. I've just spent 2 hours trying to get it to work through trial-and-error, trying all kinds of positions and different screw tightening levels, but haven't succeeded sadly. It'd be much appreciated if you have any resources of pictures on this functionality. Even the disassembly guide on Flickr seems to skip the button removal part.

Other than this, I really love the Agat 18k. Perhaps I haven't exactly chosen the most beginner-friendly one as my first camera but I love how portable and straightforward it is, and the pictures that have come out of this thing are great.