At a minimum, I’m hoping for a basic speed control.
Ideally, I’d love a way to program this servo to go back and forth like a pendulum, but have some control over the force.
My goal is to compare the accelerometers on different mobile phones.
Thank you 
Since you are talking about having sensor input, it’s best to opt for a microcontroller, which, assuming it can send RC PWM signals, can also be used to control the servo.
robotshop.com/en/microcontrollers.html
If you’re new to programming, try something Arduino-based:
robotshop.com/en/arduino-mic … oller.html
Accelerometers:
robotshop.com/en/sensors-accelerometers.html