After 30 years, IBM gave Mary a commemorative clock, after which she promptly retired. Back in the day, they used to hand out Atmos clocks (admittedly, on more momentous occasions), but this isn’t one of those. In fact, although it appears to have a torsion pendulum, that’s a separate motor-driven foo-foo which we immediately turned off:

It normally sits on the living room coffee table (which actually holds a myriad plants next to the front window) where, after we scrapped all the upholstered furniture, the two of us can’t both see the clock face from our chairs. Having a spare clock insert from that repair, we had the same bright idea at the same time: we need a clock with two faces! We came up with Janus independently…
Despite its fancy appearance, the IBM clock consists mostly of brass and plastic, so I had no qualms about having my way with it in the shop. The new clock insert spanned the clock’s gilt plastic back cover, needing only a #1 drill hole for the adjustment stem, and exactly filled the available space between the back cover and the case. Both movements had enough interior clearance for 3-48 brass screw heads and nuts, so I eyeballed the right spots on the new cover, centered the Sherline spindle on the plate, and drilled two clearance holes 6 mm in from the edges on the vertical diameter:

That put them 61.3 mm apart across the diameter, which would be awkward to duplicate by hand. Manual CNC makes it trivially easy to match-drill holes; I clamped down the gilt back cover from the IBM clock, aligned it to the table, located the center, and drilled two 3-48 clearance holes:

The glow from that polycarbonate packing block isn’t quite so nuclear in real life. The clamping force goes down the side panels of the cover, which had enough of a curve to be perfectly stable. Yes, I’m drilling into air, but came down real slow using the Joggy Thing and it was all good.
Assemble the two back covers (the holes matched perfectly), mark the adjustment stem hole, disassemble, hand-drill, reassemble, tighten nuts, and install:

It does look a bit lumpy from the side, but that’s just because I don’t have any gilding for the black tape wrap:

There, now, that was easy.