An update: I have tried this repeatedly on my 6/99 build 2000 323 Ci to no avail.
I confimed that I am indeed shorting pins 7 and 19 with a multimeter, so I know my "paperclip was good". I leave it on for several seconds, and it doesn't reset the "oilservice" miles-to-go display which appears for a few seconds after turning the key to position 1.
The two procedures I've tried:
1. Connect pins 7 and 19 together.
2. Turn key to position 2.
3. Wait several seconds (anywhere between 3 and 30)
4a. Turn off, remove key, put key in, and turn to position 1: "oilservice -#### miles"
4b. Turn off, remove key, remove paperclip, put key in, and turn to position 1: "oilservice -#### miles"
1. Turn key to position 2.
2. Connect pins 7 and 19 with paperclip.
3. Wait several seconds (3 to 30)
4. Remove paper clip
5. Turn off, remove key, put key in, turn to position 1: "oilservice -#### miles".
So there are two options:
1. This method does not work on this first build batch.
2. This method doesn't actually clear the miles to next oil service counter, and this thread is about some other light that has never come on in my car.
3. I'm missing a key step which evidently everyone else thinks is obvious.
Any advice, other than "try again", is greatly appreciated.