Bullfrog-
Just to confirm...this is an IAP network and there is no external HW based controller. Correct?
If this is an IAP only network I suspect one of two things:
1. Software mismatch between the existing IAP network and the RAP-3. By chance, did you upgrade the existing IAP network to the latest 6.1.3.4-3.1.0.0_35320 from the TAC site? If yes, when you add the RAP-3 there will be a mismatch as the RAP-3 has an older version of code from the factory. 6.1.3.4 has not been posted to the cloud servers yet so the RAP-3 cannot get upgraded automatically and the amber WLAN LED will come on..........tested this on my own setup. To fix this wire the RAP-3 to a separate network and manually upgrade the SW.
2. Do you have "Auto-Join" disabled? If yes, no new IAPs will be able to join the existing group and the amber WLAN LED will be on. If this is the case set Auto-Join to enable and reboot the RAP-3.