It seems like it's specifically with files that are larger than 1024x1024. I resized things to 1024 and it seems to work correctly, it's only 2048x2048 and larger that seem to have issues. I did a number of tilemaps of various sizes with the same filetype each time, and only 2048 and above failed to show the tile selector.
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I'm trying to use a really basic custom tileset (it's a 2048x2048 large image, right now there are only 2 tiles in it that are 512x512 each).
When I enter build mode, the tileset doesn't show up in the bottom right corner. I can draw tiles, and they're the right size, but they all just have the grey background color from my image.
I've set the world pixel density to 512 already, and the texture shows up inside blender.