The light is a LED just as the other two buttons, and the climate control illumination. If you have the chance, just unplug the connector to the Climate control Switch Module (X18151, Black 10 pins) and check the module for a LED from 6 to 7, from 6 to 5, from 6 to 3 and from 6 to 1. Switches (buttons) are from 9 to 2, 10 to 2 and 4 to 2. There is also three LED's in series with a resistor from 8 to 2. If your tester has a diode check, you can check LED's having 1.4 volts forward, open circuit reverse, if not, check resistance just as you do for a diode. The series LED's will need more than 4.2 volts source to test, not all the continuity testers feed that much, you can array 4 x 1.5 batteries and fed from 8 (+) to 2 (-) they should light up, even dimmed.
All this LED's are powered and controlled from the Integrated Climate Regulation Control Module IHKR/F3, if all the LED's are fine, the switches tested fine, and the other buttons LED's work fine, guess you have a problem inside the IHKR/F3 (doubt it).
If the defogger is permanently on, no mater the status of your switch, either you have a short circuit to ground in the IHKR/F3 output controlling K13 coil, you have a stuck close contact in the K13 relay, or some sort of short circuit in the wiring (doubt it). Just pull out K13 and push it back in, if you feel it clicking, there is a Rear Defogger request signal to the relay, if no clicking, check for open circuit between pin 30 and pin 87 of the relay, if continuity there, the power contacts of the relay melted close, if checks OK (Open circuit), and you have no click when put back in the socket (just to confirm), pull it back out and check voltage to ground from socked hole corresponding to pin 87 of relay, there should be 0 Volts, if not, there is a short-circuit to battery voltage somewhere from the defogger relay to the heating elements (doubt it as you would have notice other symptoms). Hard to tell who is the culprit, Anti-Theft, antenna amplifier?
If you have a click at the relay, then check if the click disappears when you unplug the IHKR/F3 connector X18157 (Blue 26 pins). There are two of them; you are looking for the one with a Brown/Yellow wire at pin 20. If the click is still there, you have the wire short-circuited to ground somewhere between the IHKR/F3 module and the rear seat fuse/relay box, the Brown/Yellow wire turns into a Brown/Orange one before reaching the K13 relay, check the wire from X18157-20 to K13-86b. If the clicking disappears when you unplug the X18157 connector from the IHKR/F3 module, then; there is a problem in the module as it is requesting defogger operation without the switch telling it to. Guess you did debug the proper operation of the switch.
Just let us all know what did you find out when done.
Javier
Edit: Links to missing pictures
http://www.bimmer.info/forum/attachm...ntid=851&stc=1
http://www.bimmer.info/forum/attachm...ntid=852&stc=1