I recently bought an LED "Table Lamp" with flexible neck and batteries in its pedestal, for measly five bucks.
I separated the neck from the pedestal (caution: do not cut the wires!), glued the neck stump into an empty pen handle, connected pedestal and neck with a length of wire, et voilą, a Saxophone/Bass Clarinet leak light with foot switch!
You can also attach a clipboard clamp to the pen handle and use it as marching / gig lamp. For the Sax I had to file off the head a bit so that it would fit into the neck end of the (alto) saxophone. Very bright, hardly gets warm, and batteries last (nearly) forever.