Thank you Rick! If converting to LED, as long as you can find a driver that meets the input voltage you want you can do it, well output matters too if you want to drive multiple LEDs.
I'm assuming you did already but check the bulb on that halogen lamp. The stock lamps for both my lathe & mill use 24V bulbs & they are powered directly off the 24 VAC output from the machines. The one for my lathe that died a month ago was a 110V plug-in-the-wall lamp, it still used a 24V bulb. Inside the lamp it had a 110V to 24V transformer, that's what died.
Also on Aliexpress (and ebay although more expensive) you can buy LED lamps that are already configured to run on 24V, 36V, 110V, or 240V. They don't cost much either on Aliexpress.
EDIT: N/M I think I misunderstood. Sounds like you want to repurpose it for something else & not run it on a machine?