How to drill Chinese Pietersite?

Hello,

Last weekend I found a wonderful teardrop-shaped polished nugget of
Chinese Pietersite about one inch long. Initially I’d thought of a
metal setting, but the entire stone is so beautiful I don’t want to
cover any of it. So I’ve decided to just side-drill the top for a
very simple bail.

How do I safely side-drill the top? Does Pietersite flake easily?

(I have a flex-shaft but no drill press yet, am planning to get one
this week.)

Is there a stabilizing tool that facilitates drilling evenly from
both sides to meet in the middle? I’d been planning two clay
half-molds to stabilize the stone during marking/drilling, but no
matter how I think it through, I see flaws in my plan.

Do I drill under water, or just use oil to lubricate the hole?

Thank you!
Lorraine