When you open the Cup Holder Storage Tray the LED Chip should come on and be alight with glory.
ADDENDUM:
You can easily vary this DIY by using your own version or color LEDs. Just make sure they are genuine LEDs. The technique for doing this should be the same for all E36 cars as well as other cars with a similar electrical and interior layout. If you want you can also easily add a switch for the light or add extra LEDs for rear passengers using your power/ground leads coming from the front of car. Just having the extra leads back there will give you the flexibility to add other things you may want to have in the rear of your car.
Here are the specs for the LED chip used in this DIY:
Product Number LE-MD201
Product Name Aluminum-Based Board LED Cluster White-Short
Luminous Intensity (mcd) 1400-2200
Minimum Working Voltage / Working Current / Power Dissipation DC-7.0V / 10mA / 0.07W
Typical Working Voltage / Working Current / Power Dissipation DC-12V / 80mA /0.96W
Maximum Working Voltage / Working Current / Power Dissipation DC-31V / 340mA / 10.54W
View Angle 140 degree
Temperature Rise (Test Condition: exposed in air.) 40 Celsius
Wavelength /
Voltage drop of LED 3.1v
Item Net Weight 20g / 0.7oz
Company: Sure Electronics of Honk Kong