I've got a rather nice, vintage Luxo work light--solid, stable, giving plenty of light for tasks.  It's got a T9 circline fluorescent tube around an incandescent (now LED) bulb.  The two circuits are separately wired.  The issue is, it'll intermittently shock me when I touch it.  Before I go to rewiring it to go all-LED, I'd like to diagnose the issue.

I've pulled it apart enough to confirm that neither of the two wirings' insulation have worn through at the joints.  My next guess is that maybe the ballast (transformer?) is the issue.

It looks like there was some paper insulation around it, but that's largely deteriorated.

Could the short be due to that ballast, touching the metal divider or base box?