This is a general comment since I know zero about 360’s … but are you dead sure the spinny-bit inside the cable’s turning?
I’m not sure how easy it’d be to do, but are you able to disconnect the cable & either get someone to spin the rear wheels and see that the cable is actually turning? IMHO it’s most likely the electronics in the speedo itself at fault, but it’d be good to be totally sure that the drive in the gearbox is working.
How does the cable clip into the back of the speedo? The 240 has a round plastic clip attached to the end of the cable, you push the cable into the back of the speedo then turn the clip about 180-degrees to properly attach the cable BUT it can seem like the cable’s in properly if that plastic clip is totally missing & you didn’t realise that it should be there in the first place.
Short version - are you sure the cable’s attached properly/positively to the back of the speedo?