This seems to be top secret information for some reason. There are a number of people building these but I can't find anyone talking about what they used for the guts. (Maybe I just suck at searching.)
I tried a couple devices out, but the one I found that works the best is the 2.4" landscape video business card. I got mine from Red Paper Plane as a demo unit, It cost about $30 shipped. The screen is not the greatest, I'm sure there are better clones out there, but this got the job done. If you tear it apart carefully, you can salvage everything you need. You'll probably want to clean up the wires shortening and resoldering them. I ended up swapping the speaker from a larger 3" video business card as it sounded and fit a little better. (Sadly as nice as the 3" screen was with color and contrast, it just wouldn't fit in the model with out more modification than I had time for.)
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There's a magnetic reed switch that comes with this unit I used that and (poorly) integrated a magnet to the lip of the "antenna" section, it's the out of place half-moon shape. The switch is mounted between the grill and the dials on the model. I thought the speaker (which is mounted behind the grill) would interfere with the reed switch, but it doesn't look like the magnet is strong enough.
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All of the electronic components are super professionally... hot glued into place. To hide those crimes I covered the hot glue and circuit mess with fabric gaff tape. Sorry, I didn't take any pics of the guts before they were dressed. (To be clear the wire on top is the charging / data mini USB cable, the reed switch is hidden below the tape.)
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The other hurdle is the moiré video. There are lots of good videos out there, but I had to reformat mine to fit the screen properly. I also had a very frustrating time getting the video on my device. It seems that this particular size (and this may be just this unit) is VERY picky about what formats it uses. When I say it's picky, know that I say this as someone who has access to nearly every video editing suite available, and had working source content that I could clone the size and bitrate of.
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There's one (also top secret) piece of software that Red Paper Plane is using to upload video to these units. It looks like it's from the early 2000's and is probably full of viruses (RIP my computer). It installed as "Media Player Utilities 4.46" specifically the "AMV&AVI Video Converter" in this suite is what you're going to use. There's no real setting changes you need to make, it just magically pops out a converted video that works with this media player.
Things that I wish were better:
1. The video unit take about 3 seconds to boot, which doesn't seem like a lot, but I would prefer more of an instant on.
2. The screen of my display is kind of washed out, I had to over saturated the colors on my moiré video to get them looking serviceable.
3. I need to pay more attention to the project runs so I can snatch up gorgeous machined metal parts.