No need for flip flops or any electronic parts other than some switches. Use two microswitches. On switch #1, connect the common terminal to +V and the NC terminal connects to the NO terminal of switch #2. Common terminal of switch #2 connects to one side of light bulb or LED. Other lead of light goes to ground.
When drawer is closed, one of the two switches is open and the other is closed -- light off. When drawer is half open, one switch is closed and the other is open -- light on. If drawer is opened past the second switch, one switch is open and the other is closed -- light off.