My K1200RS when ignition is turned on goes through its ABS checking routine but the ABS warning light does not slow down to the slower rate. When the front brake is applied the ABS brakes operate and the motor function is audible. When the rear brakes are applied this is not the case.
I had a BMW trained person hook the bike up to his computer and it came up with an error code 17419 but he said that he doubted that this was right as he had never seen this rear motor for the ABS fail before. I contacted a major BMW parts supplier in Australia and similarly they told me to look elsewhere for the fault as they had not seen this motor fail.
I am at a loss as to what to look at next. The alternate BMW dealer is some 180k away and I don't really like riding when the brakes are not working properly.
With this model if the power assist to the brakes fails it is almost the same as having no brakes.
Any suggestions on how I might cure this issue?

Certainly sounds like the sort of response I'd expect from a BMW crew.
Just because they have never seen one of them fail before does not mean it does not happen and to be quite honest I would be inclined to believe the error code and check it out properly before you write it down to a stupid computer error code.

One guy to ask about ABS is Tosi Tabuki in Japan http://bmwk10075abs1fix.web.fc2.com/
He mainly specializes in ABS I & II but I seem to recall that the III systems were also on the table.
BTW Marten this is a Brick 1200 not a wedge is it.

One other place that you may get good info is the Excellence in motion forum http://www.k-bikes.com/forums/forumdisplay.php?f=42

Is this a servo braked bike?

MikeP wrote:Is this a servo braked bike?

Yes and the front servo is activated when the brake is applied but the rear doesn't - it seems simplistic to agree with the Code error that the servo is broke - it might be that there just isn't power to it I suppose but I don't know how best to check all the other potential ways in which it might be broke - if I could identify a burnt or broken bit I would replace same.

I agree that it's highly unusual for a servo to fail just one brake.

The servos do need fresh fluid regularly. 

I don't know what, if anything, has been done to the bike before the issue arose but FWIW, I managed to create a problem with the rear circuit of a servo bike by inadvertently swapping the rear indicator wires from side to side (not on a K though). The rear indicators shared the tail/brake light circuit and the brake light is linked to the servo.

The servos are electric and therefore prone to odd-working if there's something amiss with the associated circuitry. Many people found that fitting an LED brake/tail lamp caused the servo to play up.

After my experience, I'd begin by checking that all is well with any wires and connectors of anything that shares the circuit.

This is from my Clymer manual don't know if it helps, It also mentions to make sure the battery is fully charged as a lot of problems seem to be caused by batteries on there way out. you could also look in this forum as well there is a dedicated forum for our K1200 RS models. http://www.i-bmw.com/index.php