THe sensor is located right behind the rear-view mirror:
https://www.dropbox.com/s/boq28rp469ry56q/E300D_Rain_Sensor_Before_Removal.jpg
Turn the mirror toward the passenger side and pull out the large round plastic cover.
The sensor has two tabs on each side (right and left). You should be able to pull them out. They're not quite visible in all picture, but some of them should give you an idea:
Once the two plastic tabs are out (they don't come out completely; I think they slide about 3 - 4mm, not more)

http://www.dropbox.com/s/pcskksfpsj43tg5/E300D_Rain_Sensor_Before_Removed_tabs_Out.jpg

https://www.dropbox.com/s/wcoyko7txp40tg2/E300D_Rain_Sensor_Removed_Tabs_Out_01.jpg

Once the tabs are out, you should be able to detach the sensor from the windshield. It'll look like part of it remained glued to the glass. Leave it there.

Turn the key to the first position where the wipers can be turned on. Aim camera at the sensor. You should see this:

https://www.dropbox.com/s/r7rgp6vjb27dw6z/E300D_Rain_Sensor_On.jpg

Turn it off: you should see this:
https://www.dropbox.com/s/jorbg4ag4s53ujc/E300D_Rain_Sensor_Connected_Off.jpg

If your LEDs are bad (which after 14 - 15 years they might be), you'll see a very dim light or no light at all coming out from the IR LEDs. Mine were VERY dim, so the only way I could see them work was by switching the ignition on and off.

Ok, I'll stop here with the write-up because I didn't get a chance to disassemble the sensor again. I'll do it tomorrow and follow up with more pics. Sorry about that.

Basically it's straight forward from here: you need to remove the top plastic cover, unsolder the LEDs and solder the new ones back in place. I gave you the part number in the original post.
If needed, I'll take it further apart and post more pictures.

Tudor