Duty cycle is not the normal way of looking at the idle circuit although looking at it with a scope can show whats happening from a qualitative view.
Because both sides of idle motor are hooked to the controller (unlike V8s which are powered on one side and grounded by the controller) current is the way its viewed. Normally the idle should be at proper speed with a current around 600ma. Adding A/C should add 50ma. Adding load, by turning the steering wheel say, should increase the current and the speed should stay the same.
As to the speed signal take a look at my other article about A/C. It shows scope patterns for the crank sensor and how it looks after the ignition changes it to a pulsed DC signal, which is used by the FP relay and the Klima relay, MAS or whatever.
Bosch Master, ASE Master, L1
33 years MB technician