How to reverse engineer a motorcycle speedometer?
Indeed, as @Passerby says, get the wiring diagram - factory service manual should have it.

If that (as it might well) leaves some parts unclear,  step 2 would likely involve some sort of datalogger connected to the wires, ideally synchronized with a video feed of the face as you take it out and ride it for a while to generate some data events, followed by sorting out what the data did when various things were done/displayed. 

You'd probably want some nice boring runs at various constant speeds to sort out the actual speedometer function - if it's "non-mechanical" in nature it's probably a combination of an engine speed sensor and a gear sensor, though it's just barely possible you have a wheel sensor (the service manual should know that, at least.) If you pull in the clutch and idle while coasting at speed, what does the speedometer do? Plummet with engine speed or reflect actual road speed?