However if I do the same for the keyboard i get the message that it is waiting for the bluetooth keyboard to connect. Then tells me that no keyboard can be found.
This is obviously not the case as I am using the keyboard to type this question.
Do you need to press something on the wireless keyboard to put it in "pairing/discoverable mode"? Ooo, just checked, I think so:
That probably explains the message. The keyboard isn't in "pairing/discoverable mode", broadcasting that's it's available. If you want to pair it again then you'll need to put it in pairing/discoverable mode, even if it's already paired. But it's something to remember if you want to pair it with another future Mac.