Runs on wide type button batteries.
when pressed on the body flexes and causes the led pins to touch the battery. That is how it is designed to operate.

Added a second version with more details.

Just two parts, the led's leads contact the battery from each side by the flexing of the sides with the push of user's fingers.

a 3mm bright led, white etc color can be used along with a 3v button cell w suitable diameter.