Yobi-tsugi : Filling in a missing piece
This method avoids using a lot of gold but looks nice.

Using tile cutters nibble the replacement piece to fit the hole.

Insert and fill the gaps with putty. Carry on with repair as normal.
​An opaque glass piece could be used so light can come through.

Then finish with metal powder. This one is 24kt gold leaf powder finish.
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No metal powder used, simple black urushi finish.