Hi,

This might be a mechanical problem.  I'm thinking it might be a loose needle on the servo motor rotor, or maybe the servo motor inside the cluster is failing.  Open the cluster and see whether the needle is secured to the rotor.  Fix it if not.

If the needle is not the problem then to confirm whether the speedo servo motor is failing will require an oscilloscope and knowledge about the UAF0115 driver that operates that motor.  It might be necessary to replace the cluster.

If the k1100rt is like the k100 RT, and it seems to be, you don't have to remove the fairing to remove the cluster, as unlikely as that seems. 

I've had your symptoms, I don't remember about the odo part tho. in my case there were three pins on the right hand side, in the cluster, fed by a ribbon from the left side, they were rusty. If yours are, you want to clean them with deoxit and the sockets, and maybe even give them a slight twist for a tighter fit. I'm not good with electrical stuff but if that's your problem it's a very simple fix.

If the k1100rt is like the k100 RT  It's not it is attached to the fairing mounting antler.
This sounds to me as if the problem is internal to the cluster and not the sensor.

Thanks for the help. I'll get into the cluster and let you know how it goes, but it won't be for a few days as we have guests staying so the bike will have to take a back seat.

How's about trying to interest the guests in taking a back seat ride on the bike. If you work your magic on them, they might even take an new interest in instrument clusters.

Not a bad idea davyson but they are just not the type.

I had a problem where the speedometer face was expanding in the heat and hitting the needle causing it to stick. Only happened when sun was shining. Normally not a common occurrence in Ireland (the sun) but showed up when I went touring. I fixed it by sticking the face down.