Harbor Freight sells
LED lights that look like wall light switches. They have screw keyholes and magnets both, so you can either put mounting screws in your cabinets or epoxy a thin ferrous plate inside. They are so bright you can barely look directly at them (in fact, they sell a dimmable model for significantly more). You can swap new batteries in when needed. They are under $4, and appear often in their coupon roster as "free with any other purchase."
(This weekend, it's the blue hand worklight that is
free with any purchase. I keep these all around my home and trailer, but I wouldn't mount them in a cabinet due to the pushbutton being awkward there, as well as the two alternating bulbs.)