The Quilting Marine was struggling this problem and found an inexpensive and effective solution. The Wenice Sewing Machine LED light strip (find it here) sheds light all across the underside of the horizontal arm of the machine, lighting up the entire bed.
The photo above shows the machine with its standard light, while the one below shows light levels with the light strip on. What a nice improvement!
The following video shows the light in action.
The bendable light strip has a sticky back so it can be affixed to the machine, can be cut at intervals to fit, and has a dimmer switch for adjusting light levels. Since it’s LED, the strip will provide light for thousands of hours of sewing.
Play with the placement of the strip to put light right where you need it. Because it bends, most likely you can apply the strip so the end sends light down toward the needle. Nice!