The emphasis shall be on the methods of wiring and testing a simple circuit. The product of this instructable is not the blinking light you build - it is the knowledge that you gain as you build this extremely simple circuit, with materials that are commonly available, with simple tools and very little specialised skills.
Step 1: Take the lamp apart
The picture shows a pen with built in LED flashlight.
Step 2: Three button cells
The three button cells are visible in this picture.
Step 4: Battery holder, LED and switch
Step 5: The switch
The second picture is that of a similiar module removed from an empty cigarette lighter tossed in my path by an unknown benevolent wellwisher. Many thanks to that magnanimous person.
Step 6: Connect wires
The idea is that you connect an electronic switch to these wires and connect the music to it so that it closes in time with the beat of the music.
Then you will have a white lamp which flashes in time to music.