The clamp holding the magnifying lamp (with a fluorescent ring light!) over the Basement Laboratory Desk finally fractured:

Gorilla Tape held the broken parts together well enough to determine how it used to work:

The two parts used to be 11.2 mm thick, but it fit on a random chunk of half-inch aluminium plate so perfectly as to constitute a Good Omen:

I decided the saw kerf would make up the difference, because, sheesh, we’re talking pot metal here.
Lay out the center, use a transfer punch the same diameter as the lamp pivot to get the proper spacing, give it a whack:

The alert reader will note I came that close to drilling the hole through the wrong side of the angle.
And, yes, extrapolating the vertical edge downward suggests the large hole-to-be will intersect the small hole-in-being. This is deliberate: the clamp screw through the smaller hole fits into a recess around the lamp pivot shaft to keep it from sliding to-and-fro. I had to convince myself, but it really did work out OK.
Pay some attention to clamping it at right angles to the spindle so the big hole goes through more-or-less in the right direction:

The masking tape serves as a depth reminder:

Set it up in a machinist’s clamp, bandsaw in twain, file the kerf reasonably flat, clamp the halves together, then bandsaw the clearance slot:

The clearance kerf wasn’t nearly as on-center as I wanted, which doesn’t really matter, but I filed a bit more diligently on the shallow side while clearing up the slot:

Introducing the new parts to Mr Disk Sander roundified them enough to pass inspection. These angular bits obviously require a bit more attention to detail:

The lamp originally had a fancy knob on the screw which never worked particularly well, so I replaced it with a nylon locking nut to maintain a reasonable amount of pressure:

The far end of the screw has a square shaft fitting into a square hole in the lamp arm, making it easy to torque the nut enough to make the pivot grip the shaft properly; if I ever find my Belleville washer stash again, I’ll add one. I should cut the screw off, too, but that’s definitely in the nature of fine tuning.
A pleasant morning of Quality Shop Time!
The obligatory doodle with dimensions, some of which turned out to be completely incorrect:

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