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Different makes? One a Nippon Seiki and the other a Nippon Denso?
Any M6 stainless domed nut should do. I don't think there's any such thing as a JIS nut, screw yes. I don't remember anything special about the 6mm domed nuts on the clocks myself. I used 6 x 18mm stainless washers on my clocks IIRC. Standard thickness.