It's most likely the wiring harness that controls the speedo. They go bad a lot and I've run into this problem a few times at work. You'll need to replace that harness. It goes from speedo and connects to main harness under the tank behind the plastic.

 

If you think of the logic of that and taking into account what hpotter said


"the battery must provides the speedo power to support the clock and display the mileage while key is pulled out.

If the bike always drains out power overnight, then the first easy thing to check probably is to unplug the the two relays and has the bike sit for 12 hours to see if power is still drained or not.."


Then you should in all likelihood see continuity through thse speedo pins as it has to have an internal hardwired circuit to provide continual power for these functions.


When you unplug the speedo and the short goes away...Does the battery drain also go away?


Your test for the blue/grey showing continuity at the fuse box is being done with the maxi fuse in or out?
The battery fuse (blue/grey) is connected to the maxi fuse which in turn is connected to the battery which obviously has a ground.


The system relay on these model bikes is notorious for causing issues and well worth removing overnight as suggested. Albeit usually on slightly earlier models it can leave the IAC cycling even at key off and cause an overnight flat battery.
Got to be worth trying before the trip to the dealer I think.