My experience for what it's worth! I experimented with two types and decided neither did what I wanted. More on that at the end!
To my lathe, I fitted a magnetic sewing machine light, like this one but cheaper.
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Prices range from about £5 to £40. They come with either a plastic clamp or magnet base, making them easy to fit to most machines, moveable, and they produce a reasonable white light. The swan neck isn't long enough, and, more important the electrics may not be fit for purpose. (The more expensive versions might be: my cheap lamp was cause for concern.) Problem is sewing machine lamps aren't designed for rough workshops, exposed to knocks and fluids, where the user is dangerously well earthed by big metal machines and concrete floors. The circuit that powers the LEDs is safe enough on a sewing machine in a dry internal room, but risky as a machine lamp. The same concern applies to other domestic lamps; are they electrically safe in a workshop?
My mill is fitted with a proper machine light, electrically safe and mechanically robust. It contains a 12V power supply driving a quartz halogen car headlamp bulb. Fixed to the machine with four bolts, so attaching it may be problematic, particularly as gantry movement limits where the base can go. From memory, about £60.
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Neither lamp is satisfactory in my workshop. They both create unhelpful deep shadows and bright reflections. So I upgraded my workshop's general lighting instead. Squeezed into a single garage, after painting the ceiling white, I fitted three pairs of diffused 60W fluorescent tubes – 360W daylight total. The lamps are positioned to brightly light everything underneath evenly: no shadows and reduced reflections.
So although occasionally useful on the mill, I don't need a machine light. Not perfect, as soon as the fluorescents pop their clogs I shall upgrade to LED – the light is better. The change was so successful I wondered if machine lamps are bygone hangovers from when factories were relatively dimly lit – 100W tungsten bulbs are about 2.5% efficient, compared with a strip lamp's 20%. My garage is brightly lit!
Dave