Just a little more. An extremely similar ashtray (said to be mid-20th Century) was offered on eBay a while ago but with no light shed on the symbols.
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My understanding is that they are highly stylised calligraphy symbols representing a ‘signature’ that even a Japanese person would have trouble reading. They might be meaningful in a modern sense, or copied from something earlier. This kind of ware was also used for incense burning in earlier times.
Just to remove any lingering doubt that the modern ones at least are ashtrays, here’s one (although with readable Japanese characters) that has two compartments intended to hold a lighter and a pack of cigarettes.
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I also noted that these things were sometimes advertising/promotional items, with one reported as having symbols that read “Hitachi Pumps” for example.