I ended up unhooking the speedo cable from the transmission - Mercedes thoughtfully provided access at the end of the transmission plate, and a hole in the plate so you can see what you're doing.

I hooked up my meter, as described, by Gilly, set on AC volts. I took my largest screwdriver and moved it rapidly close to and away from the end of the pickup. When I did this, the voltage would jump from .002 V to .005 V.

I re-installed the pickup. Since I had the car on jackstands, as a final test, I left the meter hooked up, started the car and put it in gear. Observed a large change in voltage, like up to .25 V when the wheels started to turn.

So I've concluded that the transmission and cable end are OK, and that I have speedometer problems, and am looking for someone to fix it.