Intuition tells me that 0-5v for a motor is not a sensible (purely analog) control voltage... not enough "steps" between 0 & 5. There must be more to the picture. I'de keep looking for it. See if there is not a digital signal being sent over the wire @ 5v.. +5 being a 1, and 0V being a zero.. you know the drill.
what electronics are inside the throttle assembly?
get the data sheet for the hall in question. study it. use the arduino in conjunction with that hall or some other. arduino outputs can't spoof what the hall sensor does with anything close to an acceptable degree of fineness for a throttle. Analog on/off at best from an ardie by itself
P.S. More than just hall sensor & amp, at least in this specific one. Data sheets are worth gold. The component in this diagram that you didn't mention is the reason the ardie + throttle + 5v works
arduino output voltages are very "bouncey" and not especially stable. better to use the ardie to control a dumb component that is stable at doing one simple job, in most cases.