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Not what you're asking but that static position looks fairly good: as the throttle is opened the cable will drop down to a nigh on perfect location.It seems that the heated grip was slid into place with the cable exit at (IME) an unusual angle. Personally, I wouldn't risk trying to slide the grip out, to relocate it. I realise that it makes pressing the starter button slightly awkward but consider how often that is needed. In your climate, having the cable facing downwards whilst riding is beneficial for the rain dripping/flowing from the cable. Frequently, the cable exit is found/forced in a more awkward position, risking fouling the brake lever, stretching the cable or compromising throttle action.I'd re-do that cable tie, as it's not giving any cable relief. I'm assuming the switchgear isn't properly closed up, as you were working on this.
What make/model of heated grips are they? The controller is often a clue though may have been substituted. Perhaps they are OEM ones? If so,it's very likely someone else here has better insight.
Looks like the same design as the Norge..
Yes, it is the same design as the Norge and the same controls.To fix the problem, do I need to remove and replace the grip module with a new one? Also there is no noticeable stop at the closed throttle position. Should there be any screw to stop twisting the throttle in the opposite direction?
The throttle stop is not particularly robust. You’ve to be careful when closing the twist grip against the abutment, heavy handedness will come back to haunt you.