I have a device that has a blown Daito BD20 DC400V 2A fuse. Datasheet here: https://www.furutaka-netsel.co.jp/pdf/daito/bd.pdf . These are rather odd looking, solder-in fuses and they are apparently a bit hard to find. The fuse also has an interesting internal construction; the top just snaps on so I originally thought it was a fuse holder and popped the top off. The fuse element itself appears to be contained inside of a rubbery silicone compound, and the cap contains some padding that surrounds the silicone. Is there anything special about this particular type of fuse that I should look for in a replacement?
As with many things, the answer is: Depends.
It's impossible to know what the designer's requirements are when they specced the part, so without asking them, we can make some educated guesses.
Within a certain range of products, the key specs that will matter will be current rating, and "slow blow" or "fast blow". These may or may not be written in the datasheets, but they will be shown as a time/current graph.
This seems to meet most of your key specs.