I started out with one of those magnetic lights, but found it did not have the flexibility I wanted. A dentist's light would have been ideal, but firstly they are horribly expensive and secondly they need a very sturdy mounting point in the ceiling. So eventually I built my own solution. The arm is mounted on a sleeve that moves sideways with about 4ft of lateral movement. It swings out to any angle in a near 180 degrees range. The scissor lift can be held in various place or completely relaxed to hold the lights pretty much at lathe rotational axis level (good for hollowing!) and the part holding the actual lights is fully articulated. The lights themselves also swivel and tilt in their arms, and are fitted with two LED bulbs (initially these were halogen bulbs, but they almost burned my ear off on one occasion).
Yes, this is quite a bit of work to make, but it does not require any special parts, all standard nuts and bolts and a few pieces of wood. Total cost approx. £50, plus a few hours of work, but it has solved my lighting issues for good. The workshop itself is lit with three square LED panels, daylight colour, which provide a very bright non-directional light.