Next, I disconnected the pot and replaced it with an analog protoboard adapter from Vernier Software & Technology (same wiring). Vernier sells a 3-axis accelerometer, but I just plugged in the x-axis for the first pass. The servo arm responded to the movement of the accelerometer, but I didn't have the full 180° range of motion. (Have to figure out why...)
Incidentally, I discovered something about using servo motors with the Arduino board. I knew you controlled servos with Pulse-Width-Modulation (PWM), but I didn't realize that not all digital pins on the Arduino board provided that. Only the ones with the tilde ~ next to them provide PWM. A useful tip for the day.