Assuming that one could obtain a slab of marble for the
base of a home grown bug key, is it an easy thing to
polish and to drill?

Does one use ordinary masonry drills?

Any undertakers out there?
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Yes that will do . I drilled a slate base (similar to marble ) for a pump
key .
It might be helpful to drill with the marble immersed in water.
This method also enables drilling in glass , for example to fit a
feed-through for an antenna (single glazing of course)

Frank GM0CSZ / KN6WH