There is no signal light to indicate an outdoor camera's working status. However, you can perform the following check to see if the camera is powered up correctly.
First check you have not disabled 'Automatic Camera IR' in the settings menu for the camera.
After making sure the camera is plugged in, hold your finger in front of the Infra-Red sensor below the camera lens as shown below. The IR LED's should light up faint red. This indicates the night vision IR is working correctly.
If the camera looks like the below image after holding your finger over the sensor for 30 seconds then it is likely faulty. Please open a support ticket and we will arrange a replacement outdoor camera.