You have a bad connection likely in the outside compartment. Inspect all wires and their connections to the control board.. Only possible explanation.
NOTE: this is a 12 volt issue, not a 120 volt so you can "Ignore" the 120 wires (Save for taking caution to make sure you do not accidentally connect yourself to one)
It is also possible you have a bad part on your control board
Suggestion.. If you do not find an easy fix
Get two things
1: A multiple outlet tap (Cube tap)
2: And old fashing C-7 type night light
Pull the 120 volt plug, plug in teh cube tap and then plug back in the 120 volt cord and plug in the night light.
Alternative
A proper socket and a 12 volt lamp. a 1141 should do it nicely but with a 1141 make sure the lamp socket is supported so the lamp does NOT make contact with anything else (plastic or metal) the C-7 Lamps can lay on plastic no problem.