If it's just a shallow countersink, the ideas above are fine, but looking at the pic (which isn't easy to make sense of) I'm wondering if you're looking to make a long, tapered hole several diameters deep?
If so, you might have few other options than to make a tapered reamer out of (eg.) silver steel. I'd find that pretty challenging, but clockmakers might not. Probably start the hole by drilling a series of steps with reducing diameters to carefully-controlled depths, then finish ream.
Trying to bore it would be a bit like microsurgery, but there are probably folk on here who could do it?
Edited By Mick B1 on 27/10/2020 19:30:29